How can acupuncture work on sports injuries?

Yes: If is excellent for this purpose. But - it won't repair an injury that would only respond to surgery (i.e., like a meniscal tear).

Nerve/muscle stim: Acupunture can improve acute injuries by decreasing pain and improving blood flow (leading to faster healing). It can also decrease muscles spasm. It can help chronic injuries by facilitating neuro-muscular re-integration (when there is pain, the nerves to not signal as efficiently to the muscles)- acupuncture can re-stimulate those connections.