At first, no. Later, yes.

The laws regarding slaves were referred to as 'slave codes'. They were enacted state by state, and had previously been used by the British in the Caribbean too, giving the American states the foundation for their own codes. Why were different codes needed for slaves and whites? Because if the same law was applied to both, then the "clear line of distinction [that] was needed between the two races"^1 would be lost. Without it, whites could not control blacks effectively. The laws restricted blacks from learning to read, or write; from leaving the master's property; from meeting in groups larger than eight without a white present. It's a bit of a surprise then, that after passing all these laws to restrict slaves, laws would be enacted to prevent the murder of slaves.

In North Carolina, my example state for these following paragraphs, killing a slave was not recognised as a crime until 1774. The only thing protection that a slave could claim was the legal rights of the owner to seek compensation for any slave of his that was killed. But, "such a suit was for recovery of the value of the Negro, and was not intended as a punishment."^2

In 1774 North Carolina enacted law that recognised the murder of a slave as a crime. In typical legal style, there was a staged punishment for the offence. On conviction of killing one slave, a man could be imprisoned for 12 months(which I believe in the modern United States is a misdemeanour. Yes, that's right, in 1774 you could be charged with misdemeanour homicide!) The statute got harsher though, and a second conviction was punishable by death. The law concerning murder of another man's slave was left the same, but changed in 1791 to read, "if any person shall hereafter be guilty of wilfully and maliciously killing a slave such offender shall . . . suffer the same punishment as if he had killed a free man."^3 A pretty dramatic turn around from the previous punishment of owing compensation. It was later pointed out that the new law did not provide for different classifications of homicide, namely murder and manslaughter. It wasn't until 1817 that the law was remedied to properly provide legal protection to a slave's life.

Despite all this legislation, extenuating circumstance and the judgement of the court made every case different. In State v. Weaver in 1798, the murder of a slave was justified by the master's attempt to enforce obedience. Forty years later in 1839 the court ruled that murder was not justified if it occurred through excessive punishment. This was qualified by the court saying that while punishment was necessary, if the slaveowner was found to have used "barbarous and immoderate"^4 punishment, he would be found guilty. If a slaveowner carried out the punishment of a slave with a deadly weapon, he could be found guilty, as the punishment was immediately held to be immoderate due to the weapons use.

In less extreme causes, the North Carolina State Supreme Court also ruled that "a Party having no authority over the Negro" could be indicted for assault of the man. This protected slaves from being attacked by white men who were not their owners. Their owners could not be indicted for assaulting slaves, unless they killed them, in which case it became excessive punishment.

For more case study stuff(God, being a lawyer must be tedious), the excessive punishment rulings could be mixed in with the assault laws. A white man, who was provoked by a slave, could punish the slave. However, that punishment could not be excessive. The case ofState v. Jarrott involved a white man attacking an insolent slave, before being killed by said slave. The slave was sentenced to death but the sentence was overturned because the white man had attacked the slave with a knife, which was ruled a dangerous weapon, and thus was the incorrect way of punishing a slave.

In the same way, another slave was not convicted of the murder of a white overseer because the overseer had shot him with a gun when he attempted to escape. The slave had killed the overseer, and it was ruled to be excessive punishment, and the slave was released. Coincidentally, and of no relevance to this post, the slave was later hanged for murdering a black man in Mississippi.

So, to sum up, murdering a slave was legal until 1774. After 1774 it became illegal. But it was still kind of legal because the law wasn't written correctly. In 1817 the law was fixed, and in the years following, different courts ruled on different things, and gradually a system was in place. That system was that a man who killed a slave could be sentenced to a year in prison, and upon second conviction, to death. However, the man was not guilty if the slave died after a moderate punishment had been inflicted. If the slave died of excessive punishment, which was "barbarous or immoderate", or used a deadly weapon, the killer was guilty. At the same time, slaves could defend themselves against excessive punishment, but not moderate punishment.

To answer the questions of the Op: Yes there were laws protecting slaves from their owners. If a slave owner tried to torture and behead a slave, he would be sentenced to a year in prison. If he'd done it before, he would be put to death(this is of course assuming he succeeded, and that the slave didn't kill him first).

Sources! (Both are journal articles, I'm sorry. If you're a student you can access via your college/university library).

'Aspects of the North Carolina Slave Code, 1715-1860', Ernest James Clark Jr., The North Carolina Historical Review, at Jstor.

'Towards a More Humane Oppression: Florida's Slave Codes, 1821-1861', Joseph Conan Thompson, The Florida Historical Quarterly, at Jstor.

Footnotes:

^1 Thompson article.

^2-4 Clark article.