I think most States if you just randomly murdered a slave it was indeed considered murder. However in the “slaveocracy” the plantation owners were essentially all of the local and State elected officials, much of the lawyer class would be second sons and such of plantation owners, the judges would be kin to plantation owners, all the Federal elected officials would be plantation owners etc. The Southern “slaveocracy” was the closest we had in America to the situation in the UK where a lot of power was actually still held by hereditary nobility even after the UK had technically become a democracy, the South was like that.
So while killing a slave for no reason or in a manner consistent with “murder” was illegal in many or even all slave States prosecutions would be difficult. For one, why would a prosecutor prosecute? They were cronies of the slave owners. Who would even notify the authorities a slave had been murdered? If it happened on the plantation, obviously the white overseers wouldn’t rat on their boss. The slave owner’s family wouldn’t be turning him in. And slaves would not be permitted to leave the plantation in the first place so how would they get to the authorities? If they did, who would listen? If they found someone who would listen, how would they convict? Blacks, freedmen or slave, to my knowledge, were not allowed to testify in courts in the antebellum South (I know this was true in Virginia in the late 18th century at least.)
If I had to guess, knowing nothing about it, the only slaveowners if any who were prosecuted and convicted of murdering a slave were probably the “meager” owners who ran small farms with 1-2 slaves and who for whatever reason had enemies in the aristocratic planter class who had become aware said owner had killed a slave and decided to push for his prosecution primarily out of a personal animus.
In the post war South up until the Civil Rights movement I’d say the typical response to a murdered black man would be an investigation where the prosecutor looked into it and most of the time determined there weren’t witnesses/no evidence to prosecute. The rare prosecutions, all white juries would acquit. I use the term “prosecutor” loosely as well, because I know in some places we didn’t get government employed formal prosecutors to fairly late. I think in some instances a posse or ad hoc band of citizens might capture a criminal and a judge would set a case and basically some local attorney would step up to do the government’s work on that case.