Garlic in Zone 1-2

I live in northern Saskatchewan, Canada. We planted garlic in the spring. It came up well but produced almost nothing underneath. Can i cut off the stalks, put more soil over and leave over the winter to grow larger ?

Garlic is barely winter hardy in zone 3, but you are in zone 2 or even 1. You will have to over-winter the bulbs indoor and it might be better to put them into a pot or planter box that can be moved indoors into a cool place fairly easily. Keep in a sunny window in the spring until danger of frost is past and then just move the pot out of doors. Start it in the shade and gradually move it to full sun over the course of at least a week.
Since your garlic has not formed any bulbs, this means that the growing season has not been long enough for it. You could try to extend it on the windowsill, but I would not cut the leaves, because that would deplete the roots even more.