Hayman was born in Bridgeton, Glasgow, Scotland. After studying at the Royal Scottish Academy of Music and Drama in Glasgow, he began his acting career at the Citizens Theatre in the city. At the venue, Hayman played roles such as Hamlet, the lead in Beaumarchais' The Marriage of Figaro and Al Capone. He gained national prominence playing the role of the notorious Barlinnie Prison convict turned Sculptor, Jimmy Boyle, in the television film A Sense of Freedom (1981).