What can cause mint leaves to turn red on the plant?

Red/Purple leaves on the plants represents the old leaves. These leaves must be near to senescence. ABA is major hormone leading to senescence. When a leave is under the period of senescence, many minerals are re-transported from that part to new growing leaves and the supply of other minerals stops as well. So it maybe sort of deficiency of any of those vital minerals required by the mint leaf.

This is what I have studied, about senescence in book. So I have no link for it.

It could simply be the aging process that is involved in the bright colors seen in some leaves (such as maples) in autumn, which makes the anthocyanins (red-purple colored pigments) become dominant over the chlorophyll (green) which usually produces the leaf colour. Or it could be a symptom of potassium deficiency (either in the soil, or in the plant's uptake capacity), or some other stress factor, such as inadequate (or too much) water or insect pests.

https://www.gardeningknowhow.com/plant-problems/environmental/leaves-turning-reddish-purple.htm