Garden tree roots sprouting shoots, any advice?

[Clean Rob]

I've got a small-ish (30ft) beech tree in my front garden right in the middle of the lawn. Apart from occasional trimming of the branches it's been fine for the first 2 years I've been in my house, but in the last month or two I've had a couple of shoots start coming through the lawn.

I mowed them a couple of times and they came back so I decided I've have to make a slight mess of the lawn and dig them up, when I discovered they are actually sprouting out of some of the main tree's roots (I am sure I give away my limited gardening expertise when I say that I didn't even know that could happen!)

What is my best course of action? Should I try and sever the roots that are causing the problems, or will that damage the tree itself? Is there some treatment I can apply? I don't really want to lose the tree, but the shoots are making my lawn look terrible. Any advice?

[Phisherman]

I had a sourwood tree next to my garden cut down 3 years ago. I am still cutting off the shoots that sprout in the lawn and garden. Severing roots can be harmful if you want to keep the tree healthy, but around here beech trees grow like weeds and trimming seems to have very little effect.