This reaction is somewhat akin to the one given by Kellyanne Conway regarding Kate McKinnon’s frequent impersonation of her, as Conway has similarly found the humor in some (but not all) of the sketches featuring the McKinnon character.
It’s worth mentioning that Sean Spicer doesn’t appear entirely offended by the Saturday Night Live impersonation of his demeanor.
That said, the approval of SNL is not universal, and Spicer has specifically voiced disapproval towards Alec Baldwin’s frequent and “mean” impersonation of President Trump.
Although he admittedly thinks that the series “could dial it back a bit” with regards to its satirical take on his personality, he seems to have at least partially enjoyed the comedy.