Schlippenbach started to play piano from the age of 8 and went on to study composition at Cologne under Bernd Alois Zimmermann. While studying he started to play with Manfred Schoof. At the age of 28 he founded the Globe Unity Orchestra. In 1988, he founded the Berlin Contemporary Jazz Orchestra, a big band that has over the years comprised, among others, Willem Breuker, Paul Lovens, Misha Mengelberg, Evan Parker, Aki Takase and Kenny Wheeler.
In 1994 he was awarded the prestigious Albert Mangelsdorff prize.
He produced various recordings and worked for German radio channels. He played with many essential players of the European free jazz community. In 1999 he recorded the complete works of Thelonious Monk.