Let's say this is pre-Spartacus Rome, so people aren't freaking out about slave revolts. I am a slave to a wealthy patrician. I have a good knack for negotiation from my previous life in Greece, so I do a lot of business on his account since he is Patrician and prohibited from straight commerce. Now let's say one of my frequent business associates is a slave from another Patrician family who is similarly valuable to his master. We make a lot of money for both of them. However, he pisses me off, as he constantly makes disparaging remarks about my heritage (he was from a higher social class in Greece.) Now one day, I come to do business with him, only to find him fucking a slave girl who I've had my eye on for a while. Enraged, I grab a pot and smash him in the back of the head with it, killing him instantly. A recently freed woman witnesses the event, so there's clear proof what transpired. The guy I killed was only a slave, so it doesn't seem like it would be a capital offense, on the other hand, he was the property of his Master, and valuable property at that. What happens to me now?
Most likely crucifixion.
Slaves were executed for more minor offenses such as theft, and given that the killing of a slave is essentially theft, the punishment would likley be death. As a slave, you would lack any of the protections Roman citizens do from execution, and would be crucified. Should your master have been involved somehow, they would also be responsible for paying reparations to the dead slave's owner. However, that is if you get caught. Rome (the city of Rome that is), before Augusts didn't have much of a police presence.
Sources: Bauman, Richard A. Crime and Punishment in Ancient Rome. London ; New York, NY: Routledge, 1996. Print.
Bradley, Keith R. Slavery and Society at Rome. London: Cambridge UP, 1997. Print.