Does G‑d need your mitzvahs?
No. G‑d desires your mitzvahs.

Why?
There is no why.

If there would be a reason why, it would not be a true desire.
If there would be a reason why, then the mitzvah would be no more than a means to an end, like a disposable utensil or a paper napkin.

But a mitzvah is a jewel of immeasurable value, the embodiment of divine desire.
And so the sages taught, “The greatest reward of a mitzvah is the mitzvah itself.”

For sources, see Does G‑d Need You