The depressor anguli oris muscle receives its blood supply from a branch of the facial artery.

The depressor anguli oris muscle is supplied by the marginal mandibular branch of the facial nerve.

[1] Damage to the marginal mandibular branch of the facial nerve may cause paralysis of the depressor anguli oris muscle.

[1] This may be corrected by resecting (cutting and removing) the depressor labii inferioris muscle, which has a more significant impact on smiling.

This article incorporates text in the public domain from page 383 of the 20th edition of Gray's Anatomy (1918)