No, a TVar is not a mutex guard. A TVar is a software transactional memory (STM) variable. STM works just like a database: you batch together a sequence of operations into a transaction and then execute them. During execution of a transaction, all changes made to the contents of the TVar are stored in a transaction log. If some other transaction occurs during the execution then the whole thing is aborted and re-run.
This can take any ordinary Haskell data structure and give you a lock-free concurrent data structure with easy-to-use transactional semantics. How it performs is another matter! That depends on the amount of contention and the cost of re-playing transactions.