Wouldn’t Mill have a hard time explaining DUTY – the idea that we have some perf

Wouldn’t Mill have a hard time explaining DUTY – the idea that we have some perfect obligations on actions that one never, ever is supposed to do? (Such as the negative duties not to murder or torture?) Or what about actions one must always do, such as protecting innocent human life: wouldn’t Mill have trouble explaining these as well. After all, if the outcomes/consequences of our actions always determine whether an action is morally right or wrong, can’t we imagine situations where the results of what we choose to do indicate that we’re permitted to act in what otherwise might seem immoral? That is, couldn’t murder be justified by the outcomes? Couldn’t letting innocent life perish be justified by the outcomes? And if so, then doesn’t Mill get stuck with a counter-intuitive position?
Obviously, it will be more interesting if you think Mill can make sense of such duties. But all substantive comments are welcome.