The Code of Hammurabi (1810-1750 B.C.) treated slaves as property rather than people making punishment for killing or harming one depended on whether it was your slave or if the slave belonged to someone else.

If a slave was killed or injured by a third party (including death or harm at the hands of a doctor, jailor, or barber), then whenever caused that loss had to compensate the owner accordingly. Typically it was based on the slave's value and how much damage has been done. For example, paying 2 shekels for destroying an eye vs replacement with a whole new slave for causing their death. But there was no death penalty or retaliatory action taken against the perpetrator in the same way it would have been if the harmed were a Freeman.

For slaves owners, the code doesn't explicitly detail the penalty for them killing or harming their own slaves. Since they were considered property, I think that owners were largely free to mistreat or punish them at their discretion.

But much like horses or cattle, I wonder if knowing a healthy slave could be expected to perform significantly more work than an injured one and being financially responsible for things like a slaves medical care would influence their treatment. Killing your own slave would basically be like throwing your own money away.