Should one shave or trim his beard in response to his mother's wish?

Scholars have differed on the meaning of "إعفاء اللحية" (letting the beard grow): some say it means leaving it without trimming or shortening so it can grow long, others say it means letting it grow until it reaches a fistful, and still others say it means letting it grow until it is thick and covers the jaws, even if it doesn't reach a fistful. The Sunnah of the Messenger of Allah, peace and blessings be upon him, is absolute growth (إعفاء مطلق), and this is the most deserving of being followed.

Assuming it is permissible to trim it, you are not obligated to obey your mother in shaving it, unless she has a valid Shariah-compliant reason, such as a justified fear for you, or if she would be harmed by its absence. You should be gentle with her and explain the Islamic ruling to her kindly, and pray for her guidance.