Is it permissible for someone who is praying in a congregation, and a dog appears in the mosque, to leave his prayer to remove the dog, and then return to his prayer? And what is the correct action in this regard?

Excessive movement during prayer invalidates it, and invalidating an obligatory prayer and exiting from it is not permissible except for a legitimate reason.

Expelling a dog from the mosque is a legitimate reason that permits interrupting the prayer. A dog's saliva is impure, and it might urinate or defecate in the mosque. It could also tamper with the Qurans and defile the mosque. The Sacred Law came to purify and maintain mosques. What was reported about dogs entering the Prophet's Mosque was in the early days, before the command to honor and purify mosques was given.