Cat-and-mouse meaning : A relationship in which two parties closely monitor and challenge one another in a suspicious or self-protective manner, often because each party is attempting to gain an advantage over the other. A form of attack in which the attacker toys with the victim by inflicting minor damage or letting the victim have futile hopes of escape before finally finishing the victim off. A children's game in which one player (the "cat") attempts to break through a ring of players to catch another player (the "mouse") in the centre. To engage in a game of cat and mouse.