Clearing Land

I have a piece of land on the side of the propery that is probably 300'x10'-20'. Last fall I had it mostly mowed down and looking pretty good, but this spring the weeds/vines did what they do best and grew right back (atleast this time a little thinner). Any suggestions on how to keep them from coming back.

Was thinking after they are cut down I can try tilling them out?

Any better ideas.