Layoffs in any form can be very detrimental to the Overlord’s empire. Layoffs, which include firings, and mutual separations, harm moral since friends and acquaintances are leaving, and creates a potential hole in security because of knowledge now walking freely in the open.
The fix for this is really simple, and yet current corporations cannot bring themselves to implementing the proper course of action. The proper course to follow when needing to terminate someone’s employment is to simply terminate the individual. You transfer them into a “new” department, and then, when ties to others in the company have been severed, you do the typical Evil Overlord thing, and shoot them. You can do something elaborate, send them on a training somewhere and have the plane crash, maybe make some money from the insurance issues, but that gets kind of messy.
This does not address the true issue though, and that is the problem with your hiring practices. If there is a people conflict, odds are your managers do not know how to get along with their employees, or simply do not care. And very likely, one or the other involved never should have been hired in the first place.
Granted, you should work on, and solve the underlining problems, but let us face it, you chose to be an Evil Overlord not because of you understanding heart, but because of your ruthless, bloodthirsty nature. So go ahead and terminate those employees however you see fit. Anyone who complains, shoot them as well.