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).

Hayman has also had success in directing film and TV productions. Silent Scream (1990) is a study of convicts in Barlinnie Prison, examining the life of convicted murderer Larry Winters. The film was entered into the 40th Berlin International Film Festival. Later followed The Hawk (1993), starring Helen Mirren as a woman who begins to suspect that her husband is a serial killer. The Near Room is a dark and disturbing film about child abuse and corruption set in Glasgow.

Hayman was awarded the City of Glasgow's gold medal in 1992, for outstanding services to the performing arts. In 2001 he founded the humanitarian charity Spirit Aid which is dedicated to children of the world whose lives have been devastated by war, genocide, poverty, abuse or lack of opportunity at home and abroad. Hayman is currently Head of Operations of the charity which undertakes humanitarian relief projects from Kosovo to Guinea-Bissau, Afghanistan, Sri Lanka, Cambodia, Malawi and South Africa.

Hayman is known for his role as Chief Supt. Michael Walker in Lynda La Plante's long-running crime thriller Trial & Retribution, which ran for twelve series from 1997 to 2009. He has a distinct scar over his left eye, which he chose to use as character makeup, along with a shaved head, for his part in the series.

In 2009, Hayman appeared in an episode of the BBC series Robin Hood. In September 2011, Hayman hosted a documentary reconstructing the unsolved murders of Glasgow serial killer Bible John, who murdered three young woman in the late 1960s. The documentary was named In Search of Bible John, and looked at the evidence which links Peter Tobin to the killings.

On stage, Hayman appeared as Chris in the 2011 production of Eugene O'Neill's Anna Christie at the Donmar Theatre, London. In 2012, he returned to the Citizens Theatre in Glasgow to play the lead in King Lear alongside George Costigan.

In 2012, Hayman played the Earl of Worcester in the BBC2 adaptation of Henry IV, Part I.

In July 2016, Hayman presented a BBC Two documentary highlighting Scapa Flow's key role in World war one.