How do enemy ships remove a saboteur? Do they beam them away?
Two types of Saboteur card... Non-Espionage and Espionage... the enemy can get rid of the former but not the latter. And yes, they can be transported between enemy ships.
The enemy CAN discard a NON-ESPIONANGE saboteur at the cost of the action ability which would be put into effect upon discarding the card (the same as with discarding any other crew card) (i.e., for the enemy to discard 'Ruwon', he must remove three of his control tokens from play).
The enemy can NOT discard a ESPIONAGE saboteur. The Espionage ability can only be played by the player who placed the card. Thusly the card can not be discarded [by the enemy player].
When the enemy isn't willing to pay the cost to discard a Non-Espionage saboteur or is waiting for the Romulans to activate an Espionage saboteur, the saboteur may be transported between enemy ships. From the rules: "...may be the subject of enemy Transporter actions...", and [can be] "...Transported between ships of the same fleet..."