*******SPOILERS FOR EP 4************
Well Nat obviously never told him about the events depicted in her movie and as she was the only Black Widow who turned to a hero (as far as he knows) it's the obvious thing to assume that a random Black Widow you come across is an assassin, let alone when she's attacking you.
Canonically the weapon is deadly but only when you set it on the highest power level which Natasha never did as she was a hero. As for Yelena not using lethal force on Clint I think it makes sense that she first would want some answers from him before she kills him. So my guess is she wanted to incapacitate him, tie him up and then ask him why he killed her sister.