To answer this properly we have to lay a little ground work first.

In the 19th century American south and beyond, slave owners quite literally owned the bodies of their slaves and could do many terrible things to them. Beyond the "average" depravities of beatings, whipping, and rape, slave owners had many avenues to affect their bodies. Outright murder (or something like it) was illegal most places in the American south, but most slave owners could come up with creative ways to kill their slaves if they wished. Whipping a man for punishment and then accidentally keep whipping him until he dies, or shoot them while they are allegedly escaping usually resulted in the chosen slave's death. But killing a slave is usually a bad idea. From an economic perspective slaves were one of the most expensive things you could buy besides land so people tried to avoid the death or permanent disability of their slaves unless necessary. For another, most people viewed the unnecessary killing of a slave as a moral wrong. It might not exactly be murder in their eyes, but it was a bad thing to do. At worst they might say it was simply sinful waste, and at best cruel and evil akin to murder.

So what about after the slave is dead? The master still owns their body. In theory they could dismember the corpse and do with it as they pleased, and sometimes they did. Occasionally on slave ships, the slaves who refused to eat had some of their teeth removed to allow the insertion of a metallic feeding tube. Slaves convicted of rape was sometimes castrated. A slave who ran away might have toes, feet, or even lower leg amputated depending on the punishment. Slaves accused of theft could have their hand or lower arm cut off. After a slave revolt in New Orleans was defeated the participants were decapitated and their heads placed on spikes around the town. In many ways a slaves body was not his own, but instead his masters to do with as they pleased.

But in general practice these kinds of permanent bodily destruction were uncommon. Fear and the whip were enough to keep most plantations functioning, but occasionally something more drastic was taken up to remind the slaves of the power of the master. Slave owners also felt that being too harsh might cause more revolts, which was the last thing any of them wanted. As a result most walked a fine line regarding punishments.

We're kind of going about this the long way, but we're coming to a direct answer soon. So a slave has died either through the masters doing or some other means. We've established that the master can legally do as he pleases, and in extreme circumstances does just that, typically to inspire fear in other people. So yes, a slave owner could have kept a slave's skull had he so chosen, but it would have been an extremely uncommon event. Most slave owners in the American south professed to be Christian, and keeping a human body part would have been associated with pagan cultures of African or American Indian people who occasionally did keep and trade body parts for various cultural and religious reasons. There are other cultural reasons they would likely not keep a human body part around instead of burying it.

The other slaves would have also been quite upset and the unnecessary mutilation of one of their own. By the mid 19th century most slaves were Christian as well, and the physical state of the body at death was sometimes thought to be the state it would occupy in the after life. Unnecessarily mutilating a body would have likely upset many slaves. Slave culture has its own rich history of grave rituals, and disrupting this process would have been a bad idea unless the disfigurement was part of an extreme punishment which the owner felt outweighed the negatives of the other slaves reaction. Beyond revolts, slaves had many ways to show their unhappiness from slowing work down at key times, acting in embarrassing ways in front of company, running away, breaking tools, killing animals, and so on. The only limit was their imagination and anger.

In the end most dead slaves were turned over to the other slaves to bury in an infertile patch of land on their own time off, but some favored slaves were buried in the family plot. It all depended. You can find slave grave yards all over the American south. Some slavers allowed the slaves to hold a formal funeral and provided a head stone, while others wouldn't allow their slaves to congregate at all for fear of conspiracy. If I remember the scene from the movie the slave who's skull was to be kept was a favored slave. In these circumstances they would have likely been provided with a real grave and burial clothes, and maybe a headstone. Dismemberment would have been very very unusual. The general take away is that slaves who died from typical causes were buried whole by the other slaves and favored ones were given funeral treatment closer to white funerals.

The short version? Yes, but probably not. I've never come across a record of a slave owner collecting body parts.