When an area becomes really overgrown (and includes invasives like
Ailanthus and Oriental Bittersweet) is there any real remedy except to
tear it up with a backhoe and start from scratch?

I have an area of my yard that is totally overgrown in yukka
plants,periwinkl, Ailanthus, Oriental Bittersweet, and Wysteria (and a
few others) and I just don't know what to do with it. I haven't yet
acquired the landscaping "vision". Any ideas?

-Chess