(Exodus 21:20) introduces the law of a master who strikes his bondservant: "And if a man strike his man-servant or his maid-servant." The Mekhilta explains why this verse is necessary when the Torah already addresses violence against bondservants elsewhere.
Bondservants were already included in the general rule of (Exodus 21:29): "it killed a man or a woman." A person who kills any human being — free or enslaved — is liable. So why does the Torah single out the master-servant relationship for separate treatment?
The answer is that the Torah carved out a specific leniency for the master. (Exodus 21:21) states: "But if one day or two days he survive, he shall not be avenged." If the bondservant dies immediately from the blow, the master is punished. But if the bondservant survives for a day or two and then dies, the master receives a more lenient treatment than a stranger who inflicted the same injury would.
This leniency applies only to the master — the person who owns the bondservant. A non-owner who strikes and kills a bondservant is liable under the general rules without any special leniency. The Torah created this separate section specifically to distinguish between the master's liability and everyone else's. The relationship of ownership introduced a legal variable that modified the standard penalty, and the Mekhilta carefully marks the boundaries of that modification.