Wouldnt it be better to first grow the roots till they are like 5cm(2inch) long in water before planting the cutting, or is mint really that easy? At least with some other "herbs" just putting the cuttings in dirt and keeping them wet will fail very often, and its recommended to grow the roots before planting. And ofc the roots need dark place for them to grow, so this is what i have done: take a plastic cup that doesent let light through it and place aluminium folium on it, make hole just large enough for the cutting to go through it. Also because roots need oxygenated water, i have also placed a small straw next to the cutting which i blow some air through, naturally using something like that air bubbler thing used in fish tanks would be better, but i think its bit too much for some mint cutting and other herbs can grow roots without it, so..
Also, you dont need to cut all the leaves out, its not recommended for at least other herbs. Basically the deal with the leaves is that they require energy(and not enough energy is available from a stick with no roots, so the cutting might die easily if you leave the leaves on it), but they also give energy that the plant needs to grow well. What i have done with this unnamed other herb and what i have seen others do is to leave one or two(if the top ones are really small) set of leaves that are cut in half, it stops them from growing too much for the plant to die, but also give enough energy for the plant it needs to grow roots and new leaves after it has grown roots.