Kubiszewski got his start in rock music while attending the Cleveland Institute of Music when he and a pair of classmates (later joined by Trent Reznor, of Nine Inch Nails fame) formed the new wave band Exotic Birds. The group was quickly picked to open shows for acts such as Culture Club and the Eurythmics. The band existed in several formations through the 1980s with Kubiszewski consistent as the group's vocalist and leader. The band released three albums before disbanding in the early 90s.

Kubiszewski is probably best known for his work with the band Stabbing Westward. After joining the band in 1995, he contributed to the band not only as a drummer, but also on guitars, programming, background vocals and songwriting, writing the bands biggest hit "What Do I Have To Do" (a demo clip of this song exists featuring Andy on vocals and, presumably, all other instruments).He has also contributed drums to several well known acts both in the studio (Nine Inch Nails, Prick, T.a.t.u) and on the road (Crowded House, The The).

Since leaving Stabbing Westward in 2002, Kubiszewski has been involved in a variety of projects from playing live drums with Prick, to production (including a track on t.A.T.u.'s second album Dangerous and Moving), to composing music for TV shows such as Monster Garage, Monster House, Ugly Betty, E True Hollywood Story, Shark Hunters, Johnny Zero, Queer Eye for the Straight Girl, Smallville, Lobster Wars , Access Hollywood, "Twister Sisters", "1000 Ways To Die","America's Port" and " America's Toughest Jobs". Kubiszewski has recently scored the Indie film "JAM", starring William Forsythe, Jonathan Silverman and Gina Torres. Rumor has it that new tracks have been recorded for a new Prick CD.

His new music from LobsterWars is on iTunes.