Any brushwood / bramble type killer will do the job, but you'll be left with a dead cordyline to remove but at least the roots will also be dead & so no regrowth

yes cut the new growth off and paint on something like SBK [shrub and brushwood killer] Follow the instructions on the packet.

welcome to GoY :o)

SBK yes - but cut it down and drill into the stump for about quarter to half an inch, put neat SBK into the holes, preferably without spilling it anywhere else... you can just slash into it to expose the inner tissues and apply SBK if you don;t have a drill.

I know it’s sometimes necessary but is anyone like me, hating to toss a thriving plant? I always have too many growing in pots that I don’t want but throw them out? I just can’t.

I grow many to sell at my garden meetings and talks. so I have over 300 plants to care for. I will be watering them and potting on as the summer progresses. I just hope 2021will see life back to some form of normality or at least a semblance of it allowing me to sell plants for my charities
but I agree I hate throwing plants out.