Yes you can but i like to keep them it means no risk of blocking the flue with stuff thst falls down easier inspection and many times easier cleaning from the bottom.I have a 4000 watt cadet heater downstairs and after the chimney clogged last winter I had to run the heater for a few days until I could deal with it.
It was the coldest part of the year and the cadet heater kept the house warm and only ran part of the time.
One more question that has come up in this process you guys are helping me with.
When i reline the chimney with insulated pipe can get rid of the chimney clean out at the bottom?