The term "bad mouth" refers to speaking poorly of another person, generally implying that it was done without that person's knowledge and often implying that the speaker was not truthful. This phrase is an idiom, which is a phrase that has a meaning that is different from its literal meaning. In this case, it refers to the words that come out of a person's mouth being bad, not that a person's actual mouth is bad — indeed, a person with beautiful lips and perfect teeth can "bad mouth" someone else by telling horrible lies about him or her.
Although some people might consider it "bad mouthing" even if the speaker has told the truth, such as revealing a secret about someone, this phrase usually refers to lies, half-truths or exaggerations. It often refers to instances when the speaker has done this for social reasons, such as to affect the way others perceive the person who has been "bad mouthed." Doing this without the person's knowledge — or outside of his or her presence — prevents that person from challenging the speaker's statements.
Even though "bad mouth" refers to the speaker denigrating someone else, the phrase usually is actually intended to criticize the speaker for doing so. For this reason, it is unlikely for a person to say that he or she has "bad mouthed" someone else. Instead, it is more likely for the person who has been denigrated to accuse the speaker of "bad mouthing" him or her. Someone else also might accuse the speaker of "bad mouthing" or ask why he or she did so.
This phrase likely is derived from an idiom in West Indian and African languages, in which "bad mouthing" is to curse someone. "Bad mouth" has been used in English since the early 20th century. It is believed to have first come into use in the United States among people of African descent.
Not every instance of less-than-favorable things being said about a person falls under the usual definition of "bad mouthing." For example, someone reporting another person's illegal activity or other types of rule-breaking would not be considered to have "bad mouthed" that person under the common definition. Statements that don't affect a person's social status or the perception that others have of him or her also wouldn't fall into this category, according to the usual use of the phrase.