Aside from making yard work difficult (and being a tripping hazard), my concern is that - even farther underneath than where they're obvious - they may be "planning" to create problems around of under the foundation of the house.

The other thing I imagine is if we were to somehow cut through them ourselves whether or not we'd end up killing whatever trees they're attached to.

I know we could call "a professional", but this particular job is something I'd rather be able to do something about myself.