to handle the message of truth rightly: to keep it on a straight course, neither distorting it nor veering off into novelty
This verb appears only once in the New Testament, in Paul's charge to Timothy to be a worker who has no need to be ashamed, "orthotomounta the word of truth" (2 Timothy 2:15). It is a rare and vivid word, built from "straight" and "to cut," and it survives in only a handful of places in all of ancient Greek, which is exactly why its precise force is so debated.
The picture behind it is most likely that of cutting a road: in older Greek, to "cut a road" meant to drive a straight route through rough country so a traveler reaches the destination without detours. The only earlier uses of this exact verb are two lines in the Greek translation of Proverbs, where it describes God cutting a person's paths straight (ישׁר). So when Paul tells Timothy to do this with the word of truth, the sense is to keep the gospel running along a straight, undeviating line.
The meaning is sharpened by its opposites in the surrounding verses: quarreling over words, empty godless chatter, and the false teachers who have "swerved off" by claiming the resurrection has already happened. Whatever the word means positively, it means not that. To handle the message rightly is to hold to the apostolic gospel without bending it and without inventing new doctrines of one's own.