No. The TWIC card is property of the federal government.
During the enrollment process, TWIC applicants are required to acknowledge their understanding that when they receive or pick up a new/replacement TWIC, or when their TWIC card expires, they are responsible for turning in their previous TWIC. On receipt of the new TWIC NexGen card, please send the previous and/or expired TWIC to the TSA address on the back of the card or return the card to an enrollment center.