Could it be Devil's Walking Stick? (aralia spinosa)
Try googling it and photos will pop up.
If so, I have had good results using stump killer on it. Cut the stems to the ground in the spring and immediately coat the cut ends with stump killer. It will kill them to the root.

ive also found that rock salt does alot of good when it comes to needing to kill stuff... if its a flexible thorn ive heard lime sulfur will make plants white, brittle and then it will die... im not sure if its true i bought some for my bonsai tree so i could gin it. put it on with a paint brush and cover the 1st section of it id say about to the 1st thorn depending on how spaced they are. put it on the whole thing and burn it maybe? be inventive, killing stuff is a alot more fun when youre creative! haha. you can find lime sulfur where you'd buy a bonsai tree or at lowes, home depot, that kinda place inside its usually not outside with the plants because its not supposed to get wet so yeh :)