Is my betta killing my ottos?

Betta fish are really aggressive fish and so yes they probably are killing your ottos. I wouldn't advise adding any other kind of fish with betta fish, not even a female betta would be a good idea with a male. I had a male and female betta fish and the male killed the female! Kinda weird huh? Anyway, I would get a small fish bowl for the one betta and then add some more ottos the the 10 gallon tank. If you do that you can add more fish to the tank just make sure that all the fish you put in there get along really well. I wouldn't want another fish to die. And try putting 1 fish every gallon. That gives the fish enough room and the tank isn't overcrowded.