Yes, I can tell you how to kill it!

Get some Roundup brush killer.

Get an empty, clean soda pop can.

Fill the can half full with the Roundup.

Dig a small hole near the base of a plant.

Bury the can securely in the hole and firm the soil around it - don't bury the can or let dirt get in.

Find a fairly long vine limb and cut the end off of it.

Stick the cut end of the vine in the can, so that it is submerged in the Roundup.

Secure the limb of the vine in the can with Duct tape, to keep out moisture, rain and debris. Cover the can with leaves or a flower pot, so no kid will get into it.

In less than a week, the vine should be dead. Depending on how big the root system is, it could take a bit longer, but just leave it in the Roundup - the plant will take up the Roundup and it will die.

Kayjones.. Thank you very much. I've gotten the brush killer and just as soon as it stops raining I'm going to try your idea. Thank you again so much this really sounds like it will work.

I live in NW Florida and Smilax rules our world - this is how I kill those that grow up in my yard. I have them eradicated for now, but keeping my eyes open for more that may pop up.

Kay, my hat's off to you---you are one serious plant assassin! (*grin*)

Yes, I am. I need the room, taken up by these nasties, for my ornamentals, so they have to go!