Should I purchase two lock cylinders to create a double-sided lock?
Assuming that you want to replace the deadbolt unit (as stated in the question), usually the most economical option is to remove the entire assembly including the faceplates, keyed cylinders, and the deadbolt itself (the part that inserts into the edge of the door) and replace all with a new unit.

Another option is to have the two cylinders rekeyed, if a new key is all that is desired. 

Your picture, which looks like it was grabbed from the web rather than being an actual photo of your lock, shows a specialty commercial style lock cylinder. If it is a true representation of your hardware you should visit a locksmith or commercial door and lock supplier.