Generally, 嘴 refers to mouth of all kinds animals, includes human. It's something physical. 口 is the shape of mouth, it equals to 嘴 when we want to describe mouth. But, when you want to say something non-physical,like speaking, please use 口, Besides, people don't use 口 on other animals. check the phase below, you might find some clue: 嘴唇 lips 嘴角 the crossing position of top lip and bottom lip(I don't know the correct word in English) 嘴巴 mouth 嘴型 the shape of mouth 口型 the shape of mouth 口舌 gossip 口误 say something mistake 口口相传 (message) runs from mouth to mouth 口不对心 what he said is different with what he thinks

嘴 = mouth as organ 口 = mouth as place

嘴：Colloquial, informal, 口：written language, the formal language, scientific terms

字面上讲，两个字是一样的意思，但很奇怪，这两个字却几乎不能替换使用，它们用在不同的词语里，构成不同的意思。至于在什么地方用口，什么地方用嘴，完全是语言习惯，并没有什么规律，只能靠记忆和积累。 比如： 口语，不能说嘴语 口舌，不能说嘴舌 口腔，不能说嘴腔 改口，不能说改嘴 出口，不能说出嘴 开口，不能说开嘴 嘴脸，不能说口脸 嘴巴，不能说口巴

嘴 is more verbal and causal expression.