In the film Anatomy of a Murder, on the advice of his lawyer, Paul Biegler, Lieutenant Manion elects to stand mute rather than plead not guilty by reason of insanity, despite that defense being employed. Why does he do this?
If the defendant stands mute, the judge will assume a plea of "not guilty". Therefore it has the same legal effect.
There are two possible reasons for Biegler’s advice. The first is that a "not guilty" plea would have raised even more scandal in the local community, so Biegler is trying to minimise the societal disruption.
A second, rather more tenuous, explanation might be related to the effects on the defendant's right to Clergy, and the possible effects on right to appeal (see page 513 onwards in this edition of The Complete Bill of Rights).
I think the first explanation is the most likely.