How do you deal with a cuckold slave?

It depend on who you are in relation to them. Generally, you deal with it the way you would deal with any slave. It's cuckoldry is relevant only in terms of how its spouse or partner behaves.

Cuckolds, as a fetish thing, get a masochistic thrill out of having their partner have sex with someone else. The fears being fetishized are of being rejected or betrayed by the one you love. Of having them choose someone else over you, or side with someone against you, or denying you in favor of a competitor. Each individual is different of course, but generally, cuckolds are turned on by being denied various sexual favors and activities, making ritual displays of submission to their victorious competitor, status reduction vis-a-vis the competitor (especially in the eyes or life of the loved one,) emasculation and humiliation.

General rules of humiliation apply: Exposure in public is worse than private, before people they know worse than strangers, before people whose opinions they care about for whatever reason worse than people whose opinion is of no matter to them, etc. Denial and denigrating statements are worse from someone he cares for, etc. Generally, sexual submission to another man is more humiliating to straight men than to a woman and homosexual acts in front of a woman he loves or values more humiliating still. Dressing, acting, being treated as or regarded as a female, a homosexual, a servant, a baby, a dog, etc. all are reductions in status.

The better you know the individual, the better you will know which flavors of humiliation/psychic pain is most arousing to them and what their current tolerances are before they rebel.