How can I stop my cordyline growing!

Stupid question I am sure you are all thinking, my cordyline has been planted for 17 years, it is over 30 feet tall. 3 years ago a shoot started forming near the base - this is now 10 feet tall and has flowers all of its own. Now I have 5 shoots coming out of that shoot and another 4 coming out of the main branch of the tree, when spotted the measured about 3 inches - they are now 18 inches 2 months later. My questions are this:

1. Can I safely remove these shoots and will they successfully reroot themselves by placing in compost.

2. Can I slow this down?