a strange question for garden pros but here goes

I have a problem with cordyline stricta and need to control or eradicate it in certain areas around the house as it is interfering with the foundations.

can anyone advise on the best method of control or eradication of the plant. Boy it is hardy and most control methods used like herbicides such as glysophate do not do much more than give it a cold It is crook for a week then bounces back.