Harris was born in Mufulira, Northern Rhodesia (present-day Zambia) and was resident in Salisbury — today Harare, Zimbabwe — during his active years as a driver. He is recorded with Rhodesian and South African nationality in period racing documents. He made his racing debut in 1960 at the Kumalo circuit, driving a Cooper T41 fitted with a Borgward engine, and competed in 1961 with an Alfa Romeo Special prepared by Kilner and Swift Motors, starting from the front row at the Marlborough Handicap that year.
Harris won the 1962 Rhodesian Championship driving a Cooper T53 fitted with an Alfa Romeo engine, establishing himself as one of the leading drivers in the region. On 2 December that year he qualified third for the Rhodesian Grand Prix at Kumalo and finished in the same position, behind Gary Hocking and Neville Lederle.
He then travelled south to contest the South African non-championship season opener sequence. At the Rand Grand Prix he qualified twentieth in a field of 34 cars but retired with a puncture. The following week at the Natal Grand Prix he qualified seventeenth but retired from his heat and missed the final.
The Natal Grand Prix was the occasion of Gary Hocking's fatal accident — Hocking was killed in his Lotus 24 at the Westmead circuit. The event directly influenced Harris's subsequent attitude toward competition.
After Christmas, Harris joined the field for the South African Grand Prix at East London on 29 December, the final round of the 1962 World Championship. On the Friday practice session he suffered an engine failure and missed Saturday's practice entirely while carrying out repairs. A further engine problem in final practice reduced his preparation, but he posted a qualifying time of 1:39.1 to start from fifteenth on the grid, with only Carel Godin de Beaufort slower.
In the race Harris ran towards the rear of the field, ahead of de Beaufort and Bruce Johnstone, and gained positions as retirements mounted. By the later stages he had worked as high as tenth before retiring on approximately lap 31 with a big-end bearing failure — the same mechanical problem that had interrupted his practice sessions throughout the weekend.
Following Gary Hocking's death at the Natal Grand Prix, Harris significantly reduced his involvement in motor racing and retired from competition in early 1963. He subsequently ran Alfa Romeo dealerships and later Toyota dealerships in Northern Rhodesia and Zimbabwe, operating what became known as Mike Harris Toyota in Harare. After retirement he settled in Durban, South Africa, where he lived with his wife Patricia. He died in Durban on 8 November 2021 at the age of 82.