A self-taught guitarist, at the start of the 1970s he played and recorded with the Glasgow based band Tear Gas. The musicians in that band then provided the backbone for The Sensational Alex Harvey Band (SAHB). In his white-face pierrot make-up, audiences could not mistake him, or his guitar solos on stage with SAHB.
During the 90s and 00s Cleminson played with The Party Boys, a casual band that at various times featured Marillion's Fish and Nazareth's Dan McCafferty and Billy Rankin as vocalists. This band became a reformed SAHB (Sensational Alex Harvey Band).
In 2006 he appeared in his début acting role as Wilson in the western film, A Shot in the West, for which he wrote the theme music. In early 2008 he announced his retirement from the music industry and stated he would never perform live again.