If they are suckers, you should just be able to dig them up w/ a rooted section (cut off from main plant) and have rooted sections ready for planting somewhere else. If you just want them gone, clipping them off should work, but they may come back (IE: lilacs sucker & my mom mows over hers when they cut the grass)

Hi,

I live in Naples Florida (z10) and I was wondering if there is any kind of grape that can be grown in this zone? If so, can anyone tell me their experience and possibly a location of buying grape plants in surrounding area?

Best regards,
Marius

Maybe the Muscadine type for FL? Check out Stark Bros. and a few. I have also attached a link to a web site that mentions some types suitable for Florida.

Here is a link that might be useful: Desert grape info

They may be seedlings if fruit was allowed to drop and rot in the past. In which case you should be able to just pull them up.