Cuthbert served as a Labour Party member of the National Assembly for Wales for Caerphilly from 2003 to 2016.

He was a governor of the Lewis School, Pengam, and served as principal of a part-time Adult Education Centre at Aberbargoed.

In the 2003 election to the National Assembly for Wales, Cuthbert was selected at the last minute to replace Ron Davies who stood down following a sex scandal.

At the 2007 election he successfully defended his seat after Ron Davies, challenged to regain it as an Independent candidate.

At the 2011 Welsh General Election, Cuthbert successfully defended his seat once again, after another challenge from Davies, who this time stood for Plaid Cymru.