The phrase "be sadly mistaken" is a colloquial expression that means to be completely wrong about something. There are several synonyms for this phrase that can be used in order to convey the same meaning. Some of the synonyms of this phrase include "misunderstand," "erroneously believe," "incorrectly assume," "delude oneself," "have a false notion," "make a wrong guess," "misread the situation," "get it wrong," "be off the mark," and "be in error." These synonyms for "be sadly mistaken" can be used interchangeably in context, depending on how the speaker wants to convey their message.