Are you planning on collecting and then cutting back? Maybe you could do the cutback in the ground and get it next year instead. I imagine it would respond well to that as long as you don't take everything off. I know American and Eu beech are not the same, but do respond similarly (they are cranky) so take a look at Harry Harringtons website for collection and cutback advice.
Oh and I know that to everyone else I sound like a broken record, but please put your location in your profile so good advice can be given for your climate.
I would be very careful about using collecting advice for American beech based on European beech. American beech is a more conservative tree and tends not to respond as quickly or as vigorously as European beech.
I would inspect the tree's root system before cutting roots. I have found that American beech trunks can actually be part of a larger nearby tree's root system--which means there might not be any smaller roots directly underneath the trunk.
In general, I've found that a few eastern native trees, hornbeam and beech in particular, don't do well if trunk chopped and left in the ground. This can depend on local conditions, but I've seen chopped trunks that are left to grow out in their locations just give up and die. Beech can push new growth sometimes, but it can also lose considerable pieces of the trunk while it's doing that.
