Mahou Sensei Negima!: there are two classes of normal mages. A "Wizard" focuses on attack magic while others protect, whereas a "Magic Knight" fights up front and uses spells. Negi chose the latter, but Yue has chosen the "Wizard" style complete with the Final Fantasy style Black Mage outfit.
Although Kagura from Inuyasha has shown herself to be very fit physically (being a demon, it comes naturally for her), she always fights using wind-using spells and magic. She also has no issues cutting up your best friend and then turning them into a zombie to lure you into an ambush.
In Slayers, black mages (like Lina and her sometime-sidekick Naga) are specifically wizards who call on Mazoku for their spells; both they and shamans (like Zelgadiss) can get very, very destructive effects. In fact, many "elementally offensive" spells, like the classic Fireball, are shared by both forms of magic.
Hayate Yagami of the Lyrical Nanoha franchise, who as the Queen of the Night Sky, comes with the widest variety of nuke-level offensive spells in the cast. These range from releasing city-wide spheres of darkness to creating massive icebergs that dwarf space ships.
Trisana Chandler from Tamora Pierce's Circle of Magic. This is actually a downside of winning the Superpower Lottery: Her extremely powerful weather magic (where "weather" also includes natural disasters) would put her in high demand as a war mage, but she'd prefer to be a healer, something which she's simply too strong for. To paraphrase, "it would be like performing surgery with a mallet."
All four kids, and some of their students, can put their magic to spectacular offensive use when they need to, though Tris is the most naturally suited to it.
The BBC/Starz series The White Queen portrays Elizabeth Woodville, queen consort to Edward IV, as a witch with actual supernatural powers. Throughout the series, she is able to call down terrible thunderstorms on her enemies at strategically critical moments, cause her enemies' deaths through magical curses, and otherwise wreck terrible destruction with her magic. When her husband, King Edward, lies dying of a fever, another character, Margaret Beaufort, says that the king will be fine because the queen will just brew some magic potion to heal him. Needless to say, that is not one of Elizabeth's powers, and Edward dies. That being said, Elizabeth (and her mother and her eldest daughter, also portrayed as witches) are shown to have some non-offensive powers, including divination magic; also, Elizabeth did use her magic to make Edward fall in love with her in the first place, or at least to help the process along. Still, it would appear that the Woodville women in this show are at least partial examples of this trope.
Norwegian black metal band Emperor take this literally in one of their most well-known songs, I am the Black Wizards.
Subverted in Magic: The Gathering – since the objective is to defeat your opponent in a magical duel, every player is by definition one of these. Played straight in casual team variants, where one teammate can dedicate himself solely to being The Medic.
Ammo: Almost every player character that knows magic at creation will use an offensive spell (Air, Water, Earth or Fire). Learning more elements later is helpful because of Elemental Rock-Paper-Scissors being in effect. The fifth option is Life that, while loved by the team, is serious crap for the character himself. ALL demons that know magic will spam elemental attacks like rain at a funeral.
Mages fulfill this role. No self healing while nuking from a distance.
Warlocks are also a "nuking" class. Heck, two of their specialization trees are even named "Affliction" and "Destruction"! They do have a few healing spells, however. One is where the Warlock sacrifices some of their health to heal his/her demonic minion, another is a channeled spell that drains the health of an enemy, and another is conjuring items that can heal an ally or even give them a means of recovering from death.
In Dragon Quest VIII, Jessica fulfills this role till late in the game when she gains pretty decent healing spells.
In Dragon Quest IX, the Mage class has all attack magic with a few debuffing spells overshadowed by the Sage class which has both better attack spells and gets healing spells, though the mage gets better stat growth for casting offensive spells.
Disgaea has both male and female magic users (they're coloured differently according to element). They learn spells of increasing power and area of effect that deal damage within their element (so fire mages learn fire, mega fire, etc; ice mages learn ice, mega ice, etc and so on). The highest level mages can learn most of all the elemental spells, but cannot master the strongest spells of each type.
They both use damaging spells and for the most part perform no healing or support spells. The Wizard branch uses area spells with special effects like a chance of stun or freezing and the Sage branch can cast two streams of bolt spells at once with Double Cast as well as endow weapons with an element to increase weapon damage.
In Recettear: An Item Shop's Tale there's Calliou, the Squishy Wizard who has a grand total of one utility spell, with the rest being solely for offense and no melee combat ability whatsoever. To a lesser extent there's also Arma, who's later weapons are pretty much Magitech WMDs.
Aion: Tower of Eternity has the Mage Class, which at level 10 branches off into either the Sorcerer (Direct Heavy Damage, AOE Damage, Crowd Control) or the Spiritmaster (summons pets, not as much direct damage)
Shadow Era's Mage Heroes (both Human and Shadow) are this.
La Tale has the Sorceror class, one of the two advanced classes after Wizard, which abandons all healing magic for pure offensive magic.
Imoen from the Baldur's Gate series, a friendly and upbeat sort who starts out as a thief in the first game but then becomes a black mage.
Rune from Phantasy Star IV is a full-on 'blast everything until it dies' type, whereas Kyra is a warm and friendly sort who appoints herself Cool Big Sis to the hero but can still blast things (and heal a bit).
Paula from EarthBound. She uses offensive spells such as PK Fire and PK Freeze. Kumatora from Mother 3 also fits.
Gwen, an NPC in Guild Wars, is first encountered as a happy-go-lucky little girl who befriends the player in an idyllic countryside. Fast-forward eight years of game time, and she's a powerful Mesmer described as being driven primarily by hatred and anger.
Dragon Age II has Merrill, who despite being much nicer than Morrigan, practices Blood Magic which is considered one of the most dangerous forms of magic, and has no healing magic other than using said blood magic to steal others' life force for herself.
In Dragon Age: Origins, although you have freedom to spec her as you wish, Morrigan starts off as a Black Mage as well. It's also possible to turn the player character, The Warden and Hawke, into Black Mages as well in both games.
Mallow from Super Mario RPG is another "somewhere between this and The Red Mage" example. He gets an early healing spell, but that gets eclipsed once Princess Toadstool joins you, and his specialty is in combat magic and rounding out the party's Elemental Rock-Paper-Scissors with Mario (between the two of them you can take advantage of every elemental weakness in the game).
Adepts in the Mass Effect series focus on devastating and disabling enemies using biotic powers. Recurring squadmate Liara T'Soni is a prominent Adept, with Jack in Mass Effect 2 also qualifying.
At the beginning of Duel Savior Destiny Lily is the strongest member of the Savior class, but she looks down on healing magic as worthless. This really comes back to bite her in the fifth chapter when the regular healer is incapacitated and she can't heal her or the other injured people, thus forcing what remains of your party to retreat, apart from Rico. Apparently, it's actually rare to see mages who specialize to this extent in pure combat and within a few more chapters she has begun picking up standard healing spells.
The elemental magic skill tree in The Secret World is dedicated primarily to blasting anything and everything into little pieces. Not that the other skill trees don't have perfectly viable means of damage-dealing, either, but they're often a little more diversified. Elementalism is classic Black Mage material.
On the subject of liches, Xykon in The Order of the Stick — other than the occasional hold spell, he tends to leave all non-hurty spellcasting to menials.
Vaarsuvius was initially this, mostly going for powerful and destructive spells like Fireball. However, after a brief stint as evil, a chat with Xykon of all people, and a Heroic BSOD, V is trying to be a little more rounded, creaitve, and strategic, and use support spells more. It was off to a rocky start, but helped with the return of Zz'drti.