Mary did her part of job by sweeping and by washing the clothes.

Mary did her part of job by sweeping and washing the clothes.

As far as parallelism goes either way works equally well. If you're concerned about people thinking that Mary was sweeping the clothes you might follow RubyRed's suggestion. Personally I don't think that any reasonable person is going to come up with a picture of Mary sweeping the clothes but you could recast it by reversing the order of the objects of the preposition: Mary did her part of [the] job by washing the clothes and sweeping.

The addition of the before job would be required to make the sentence good English, but that's a whole nother question.