The literal meaning of βάλλω in ancient Greek was: throw something (usually a weapon, for ex. an arrow) to somebody. Gradually it ended up with the meaning "beat", "hurt" somebody by throwing something against him.
It's meaning went even further. It started to mean "cause damage to someone's personality, not only to his body."
"δια" means inter / through and it indicates something that happens in an indirect way, not straight forward.
So "διαβάλλω" ended up with the meaning "cause damage to someone's personality by spreading lies or in other indirect ways".
In other words “διαβάλλω κάποιον" means "slander", "defame somebody".
This is how the verb διαβάλλω took it's negative meaning.
It's worth noting that the word "devil" in Greek is "διάβολος", which comes straight from the verb "διαβάλλω".