Well you have to use the preposition 'by' twice, or it will look like Mary is both sweeping and washing the clothes....the clothes being your only subject with two verbs.

What *I* would do, were this my sentence, is to write it differently:

Mary did her part of the job by doing the sweeping and the washing.
or:

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

Both of those modifications balance the verb and the subject clauses equally.

OR, I might even write it like this:

Mary contributed to the work load by sweeping the floors and washing the clothes.

However, I will defer, again, to the more knowledgeable posters here, regarding correct sentence structure, as it has been too many years since I have dissected a sentence!