Cable once had an evil clone named Stryfe. This evil clone captured Cable's wife Aliya and raped her, leading to her having a son that, while genetically the same as if it had been Cable's, was not his son. Cable had a lot of issues with the boy; it got so bad that Professor X called Cable on it when Cable referred to him as "Aliya's son" at one point.
Vivisector's father insists that the fact that Myles is his son is "a matter of opinion". Why? Simple - Vivisector is a gay mutant. Joining the X-Force was evidently the last straw, because by becoming a celebrity daddy couldn't pretend he didn't exist anymore.
Played for Laughs by supporting character Lacuna, who actively tries to get this reaction from her parents after discovering she's a mutant. When they accept her mutation with open arms, she tries to join the X-Force... and they're supportive of that, as well. Finally, she becomes a talk show host, squandering her incredible gift by chatting up celebrities. All she ever wanted was for her parents to be disappointed in her. Because how else do you know you're doing the right thing?
In Magneto Rex, Quicksilver is captured by a rival faction and Rogue asks Magneto to organize a rescue. Magneto flatly tells her that since Pietro keeps refusing to join him in ruling by his side, he has no son.
This is a large concern for many young mutants, but a particular standout would be Surge from New X-Men. When her father finds out that she's a mutant, he disowns her, because he "doesn't believe in mutants." When she tries to get back in contact with her family, in particular her little brother, he basically says that she's not his daughter. It should be noted that this is entirely on his part, as her mother is just relieved that she's safe and learning to control her abilities.
Renee Montoya's parents disowned her when Two-Face outed her as a lesbian and she admitted it to them in the Gotham Central arc "Half A Life." Her father appears in a later arc; from the look on his face when he sees her, he clearly regrets what he did, but by that point Renee is understandably unwilling to have anything to do with him. They're able to make up before he passes away in Convergence: The Question #2
In the initial "Moon Knight" series, Marc Spector (Moon Knight) has this in his background. It happened after he one-punched his father, which should count as some sort of justification.
In V for Vendetta, Valerie brings her girlfriend and tells her parents she's a lesbian. The parents were furious and scream at their daughter to leave the house. Then, the mother, in tears, grabs a picture of her daughter when she was young and throws it in the trash.
Iron Man: Tony Stark's verbally and emotionally abusive father, Howard Stark, is brought back in spirit while Tony is trapped in Mephisto's Realm in the Iron Man: Legacy of Doom run. After cruelly and viciously castigating Tony, Howard sneers, "You're no son of mine."
Green Arrow threw out his ward Roy Harper when he discovered Roy was a heroin addict and called him a no-good punk, then later acted proud as if he was responsible for Roy going cold turkey and beating his addiction, when it was really because of Black Canary and Green Lantern. Much later, after Roy's arm was cut off and his daughter was killed, Roy angrily lapsed into being a drug-addicted anti-hero before he was found and knocked out by Dick Grayson. When he awoke, Roy discovered he had been strapped to a bed in St. Virgil's, a center for supervillains with substance abuse problems. Dick had done this with Black Canary's consent, who later flat out said that Roy was beyond help and washed her hands of him.
After Klara Prast began talking to the plants on her farm (and they started responding), her religious asshole parents not only disowned her, they sold her to an alcoholic creep who took her off to America to be his wife... at 11 years old. All manner of physical, emotional, and sexual abuse ensued. Thankfully, she later befriended the Runaways, who took her off to the future, where her asshole parents and abusive husband were both long dead.
Parodied in The Bojeffries Saga in which Reth Bojeffries was disowned by his entire family after achieving literary fame with a memoir all about how much he hated them. When they're brought together again, they aren't reconciled. Instead his Uncle Festus kicks him to death, with the others' reactions ranging from apathy to And There Was Much Rejoicing.
In Booster Gold's origin story, his mother disowned him when she realized that he was gambling, much like his father was. In one account, he took up gambling in order to pay for an expensive medical procedure to save his mother's life, which made the disownment much more heartbreaking, with his mother saying she would rather have died than live to see her son take up gambling for any reason.
In the origin story for Captain Klutz, Captain-to-be Ringo Fonebone's father says this of his useless comic-book obsessed offspring.
The Spider-Man arc "American Son" ends with Norman Osborn loudly declaring that Harry Osborn was not his son, when Harry sided with Spider-Man against him. Considering that this came directly after Osborn attempted to have Harry killed in an effort to gain public sympathy, Harry didn't object. Recently, before he started working for Peter Parker's new company Parker Industries, Harry legally changed his last name to "Lyman", after his mother's maiden name.
Three: When Nestos returns home after he's denounced as a 'Trembler' (an outcast of Spartan society who showed cowardice) for failing to kill the Helots who killed his father, his widowed mother declares that her son never returned home and considers the man standing in front of her lower than her racing horses.
Invoked in Superman story arc New Krypton. When Superman and his aunt Alura are on the brink of fighting, Supergirl tries to calm her mother down... but then Alura threatens to disown her daughter if Kara doesn't stand with her.
Copperhead: After his selfish actions result in his family being murdered Floyd Sewell is exiled by his mother with this line.
The Sandman: Orpheus and Morpheus go through a mutual one. Orpheus refuses his father after Eurydice dies and Morpheus tries — in his own way — to encourage him to live on. This wounds Morpheus' pride, so he ends up reciprocating. It takes the two roughly two millennia to so much as talk with each other again, at which point both have matured considerably and are able to reconcile.
In the X-Men storyline "Grey's End", Elaine Grey, Jean Grey's mother, curses both Jean and Rachel with this before she is struck down by a Shi'ar Extermination Squad after the group murdered every last Grey.
In Chassis, Sabotage was initially banished to America by his wealthy, traditional father: essentially becoming a Remittance Man. However. Sabotage's antics eventually become so extreme that his father disowns him altogether. Sabotage doesn't care.