Help/advice needed

Hi, I planted a tree a few years ago ( I don't know what species it is ATM, but it's supposed to grow small orange berries or something in fall) and it was growing at a decent pace, but now some idiots have kicked it or something and broke it. There is a small stump sticking out which will hopefully start growing again, but I want to know if it's possible to save the top part of the tree and make it grow roots again somehow. I know some plants can do this, but I don't know if this happens with trees and if it does, what process to take.
I have hacked off the end of the trunk so it's level as someone told me to do, and then put it in water for a few weeks. The person who told me to do this said roots would start growing in a few weeks, but after 3 weeks there doesn't appear to be any sign of roots regenerating. The leaves aren't looking that good either. Is it still possible to save this tree? Should I plant it in soil perhaps? All help is appreciated and I hope I'm asking this in the correct group because this is the only plant one I could find.
P.S. What is this process of roots growing from the bottom of the trunk/stem (when there's none there) called because I couldn't find any information on the net when searching?
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ATM,
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It is close to impossible that your tree top will survive unless we are talking about something less than the diameter of a pencil with only a leaf or two. While it is very common to propagate trees and shrubs from cuttings, even that needs to be done in a well controlled manner to be successful. Frankly, I would dig out the stump and start over. This time you might consider surrounding the new tree with a guard if it is likely to be subject to abuse. Nurseries in my area are putting their trees on clearance right now, so you may be able to find a bargain. Fall is probably a better time to plant if your area has hot, dry summers.
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