The first carbon tube I ever made I did what you have done. I separated the tube and mandrel with two vehicles. I got them apart but broke the tube in half in the process.
Since then I have made quite long carbon tubes of various diameters over mandrels and had no problem removing them, but I coat the mandrel in candle wax. Just melt a candle and apply the wax with a brush and use a wide flat metal scraper that I heat to smooth out the wax out.
(Usually set up a way of spinning the mandrel with a cordless drill on very low speed to apply the wax.) When it is time to separate just poor boiling water down the mandrel tube, the wax melts and the tube slides out easy. Only issue is the wax will shoot out the ends when the boiling water melts it and if you want to bond the tube to something else you need to protect it from getting covered in the melted wax.
What is the diameter? It is just that I have also made a collapsible mandrel recently that worked well also.
I have also made them by inflating a bag inside the laminate inside a pipe that has been split and held together with hose clamps. It all depends on what I want to use the tube for in the end.