Old Apple trees

[Oregon_Rob]

I have some old apple trees that drop their apples every year and make a big mess and I want to take them out this fall. Right now, the apples are small 1-1 ½” and I was wondering if there is a way to kill the tree and get them to stop growing? If I ring the base of the tree (cut the bark all the way around), will the trees die?

Thanks in advance

Rob