Spirit Mutation happens most commonly when parents with different spirits have children. The child of the two parents will either have the same spirit(s) as one or both parents or a spirit mutation occurred, making an entire new spirit. It can also occur in other ways.
One of them is by absorbing a spirit soul or eating heaven and earth treasures. Another way is getting exposed to an external factor like a bloodline, which is the case with Tang Wulin and Tang Xuanyu, or destruction energy, in the case of Xu Lizhi. Many examples of this has occurred in the novels and manhua.
Some notable examples included: