...will it remain alive and shoot up new sprouts? What's the likeliness that the tree will end up dying? And when is the best time to do this? ( I'm assuming dormant periods ) Thank you
It rather depends on which tree it is. Some trees will take coppicing, other would just die. Which tree did you have in mind? How big is it ( Diameter of trunk) http://en.wikipedia.org/wiki/Coppicing
I have seen a version of this technique recommended for creating a Japanese Maple with a long straight trunk (but have not used it personally): After all the leaves have fallen in the Autumn, cut off the stem 2 or 3 rings above the graft point. In spring the plant will shoot from the dormant buds and one can be chosen as a leader and staked upright for the first year. All other shoots and obviously any from below the graft should be rubbed out, and if you desire the long straight trunk all side shoots too during the first year. It is reported you can grow a 5-10 foot stem in one season with this method. A strong healthy root system is a must to start with, and the minimum recommended original trunk diameter is half an inch. (I didn't notice a maximum recommended diameter, but assume the technique is usually used on relatively young trees.) As Silver surfer says, not all species would adapt to this process.
There's also a high likelihood that many or most of any sprouts will be from the rootstock below the graft. This is what happened with a big old Silver Lime Tilia tomentosa (about 25m tall, 70cm trunk diameter) that broke in a gale in my local park. When park people cut it up, the stump was left, cut about 40cm above the graft line. The next spring, about 70-80% of the sprouts were Common Lime Tilia × europaea from below the graft, and they also grew faster than the Silver Lime sprouts. Over the next few years I quietly trimmed away the Common Lime sprouts to leave just Silver Lime.
See what others have to say. I would say definitely not. As Michael has already said you would get a very odd shaped cherry. It would leave the tree very vulnerable to getting disease, which they are prone to get at the drop of a hat. I would cut it down, grub the roots out completely and plant something else there, rather than attempt to coppice it.