Feiss was born in Sacramento, California. He joined Hanna-Barbera around 1978 while still a teenager.
He worked on the 1980s revival of The Jetsons, was a key animator on the Jetsons movie, co-animated the Ren and Stimpy pilot "Big House Blues", was an animation director on The Ren & Stimpy Show during its first season and created the Cartoon Network original series Cow and Chicken and its spin-off, I Am Weasel. Feiss stated that The Adventures of Rocky and Bullwinkle and Friends was the primary influence for his work. On his shows, David directed every episode and also worked as a writer, his writing credits usually collaborated with Michael Ryan.
Feiss co-directed the animated segments of The Adventures of Hyperman, a computer game released in 1995 by IBM.
In issues #5 and #30 of his cousin Sam Kieth's comic book The Maxx, David showcased his work with The Crappon (which looks like the Warner Bros. frog mascot Michigan J. Frog), Fred Flower and Uncle Italian Moose, which had a very similar style to Cow and Chicken (they are reprinted in Wild Storm's The Maxx Volumes 1 and 5 trades). Feiss also collaborated with Kieth on a story featured in Parody Press's 1992 one-shot comic book Pummeler, spoofing Marvel Comics' famous character The Punisher.
In 2006, he was the head of story for Sony's first CG animated film, Open Season.