In 1968, McDiarmid received a gold medal for his work from the Royal Scottish Academy of Music and Drama, the first of many recognitions given to him for his work in the theatre. Soon after, he decided to pursue a career in the theatre instead, and took acting training courses at the Royal Scottish Academy of Music and Drama in Glasgow. However, fearing his father's disapproval, McDiarmid attended Queen's College, Dundee (now the University of Dundee, but then a constituent part of the University of St Andrews), where he received a Master of Arts in psychology. I said to myself, 'I don't know what this is, but I want it.'' In 2004, he stated, 'It sort of fascinated me, and it also scared me.

He became a theatre aficionado when he was five years old, when his father took him to see an act named Tommy Morgan at a theatre in Dundee. McDiarmid was born in Carnoustie, Angus, Scotland, on 11 August 1944.