Is the tree in already? If not, just tear up the turf and turn it upside down when you plant the tree, then mulch and plant over it.
Mint will spread by runners, faster or slower depending on how suited it is to your climate. It does like
water and will compete with other plants for it. I generally prefer to keep it contained, but sure you can chop & drop (smells great!). It's certainly easier to control than most grasses.