Yes, you can generally remove the fireplace. The cost of it will depend on the amount of work required for the removal process. Those who choose to remove just a few selected parts of the system will bear a smaller cost, but for complete demolition, the charge will be high. Few tasks can be done for around $1000, but for a complete demolition; it will cost nothing less than $10,000.
The different factors that you need to take into consideration while setting the budget for the removal of your fireplace are- structural considerations, materials, finishing, and the number of fireplaces.