I'm pretty sure a diamond cut into an arrowhead would more than likely shatter upon striking.
Diamonds are very HARD, but hardness isn't the same as strength. It's like titanium. It's very hard, but unless it's mixed into an alloy, pretty much crap for building anything. Why? Because it's TOO hard. Instead of giving in any direction, it just shatters.
"Diamond Tipped" saws and the like have pretty much "diamond dust" on the blades, which takes advantage of diamond's great compression strength and the myriad little edges to grind away material. On a minute level it's not so much "cutting" as it is "grinding" along a very thin line.
--fje