I'll keep no more cats than will catch mice.

The speaker will not maintain cats that fail to do the job for which they are kept. Their place depends on whether they catch mice.

Figuratively, the proverb favors usefulness over mere presence. It expresses a refusal to spend resources on people or things that make no practical contribution.

Use this proverb to express a firm, practical decision to keep only what does useful work. Applied to people, it can sound harsh, so it suits a blunt judgment better than a gentle suggestion.