@Giga - I have no disagreement with any of the content of your post. You did outline the mistakes. But I am going to share my thoughts as to what to do with the tree he already has sitting in front of him. Yes, I myself you not have collected this one. I would have collected a tree with low branches, and did the chop above the lowest branch or two. Actually, I'd shoot for at least 3 low branches, if they were all on different sides of the trunk, then chop just above those. But that ship has sailed. Deed is done.
@Aiki_Joker - Giga was telling the truth, this was a poor choice for a tree. Without any low buds, low branches, and with the fact that weather could drop below freezing, the chances of survival are already down to significantly less than 50:50. But there still is the odd chance it will survive. It will require several years to recover. Do move the tree to a location where it is shaded for the majority of the day, that will help.
If you collected this only a few days ago, cutting again, lower would not really be a separate trauma. Do seal the cut, it can be months before the tree actually produces a bud, an unsealed cut will allow too much moisture to escape. If more than a week has passed, do the second cut in 2 to 5 years. If done several years from now, never cut lower than a branch with buds. You may have to sequentially cut to a low branch, wait for buds to sprout lower & develop into branches that can support the roots, then chop again to the new lower branches. This could be a decade long process. My thought on recutting now is that the second lower chop would eliminate the decade of trying to fix having chopped too high. If the tree dies because the trauma of the second cut, or insufficient stored resources, the death of the tree will have saved you from a decade long exercise in frustration getting branches low enough on the tree to do anything with. If you cut lower now, and it lives, you are ''ahead'' by a 5 years to a decade of where you would be if you did not do a second chop. In the future, remember for beech, be sure to keep a low branch and second, the lower you are able to chop, the more time you will save yourself down the road. Keep the guideline that you want to chop lower than one third of the final height of the desired future tree.
It is far better to walk past a beech with no low branching. Where for most other species the lack of low branching is not as big an issue.
If it has been more than a week since collecting the tree, do not do the second chop. It would take chances of survival from poor to near zero.
I did have a chopped beech sit until middle of July without a single bud sprouting - actually I had several, 2 out of 3 just died even though I waited over a year for them. But one beech did sprout a couple weak buds, that developed into a weak branch, but it did live. So I would not put it on the ''burn pile'' until about 16 months months after you collected it. If it hasn't sprouted by August, it is very unlikely to ever sprout, but there are unverified rumors of trees of different species sprouting more than a year after collecting. Besides, if you wait 16 months before burning the stump, it will burn better.
If it does sprout, it will be weak. do not do any pruning or other bonsai technique for at least 2 years. Wait until you have good, healthy growth.
Hornbeam (carpinus) have a better chance of surviving this type of treatment, I have chopped Carpinus to just a short trunk and a nebari, and had reasonably good back budding. When I initially replied I had Carpinus in mind, as I had collected these more recently than my beech. Beech is definitely an exception to the ''normal'' behavior for the more common deciduous trees like elm, maple, hornbeam & hawthorn. In North America, it is fairly common, that if a forest has beech, scouting the lower depressions, more moist areas, of the same forest you are very likely to find hornbeam. Sometimes they are found together. Hornbeam is an easier tree to work with than beech, yet has similar bark and can be trained to similar styles. Keep your eye out.
Was surprised how fast this came out. I been researching digging trees for a while but 3 years away so no access. Mind you I had a good spade, I'm pretty strong and used levers. 
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