He paid a lot for the taxidermy and wanted to show it off.
The leopard killing the gazelle is from the San Juan Wildlife Museum, a city-built museum with hundreds of exhibits on African and North American animals (most of the taxidermy was donated by a local hunter who was looking for a forum to show off his kills) that was inaugurated this year. Mayor Santini has been promoting the museum so as to increase (paid) attendance and show that the city’s investment paid off not only with respect to educating kids (its a popular field-trip destination), but in attracting tourists and maybe even turning a profit.
Apparently the Mayor sent out Christmas cards with different pictures of his family taken at the museum, some standing in front of stuffed and mounted bears, and this one in front of the leopard killing the gazelle. This particular one may not have been the most appropriate for a Christmas card, but Mayor Santini probably included it because he or one of his kids liked that exhibit.
I don’t know if Mayor Santini is a hunter himself, but he is an avid gun enthusiast and a conservative Republican, and was targeted by the Brady Coalition in his 2004 reelection for being the mayor of the largest U.S. city (San Juan’s population is around 425,000) to have supported the repeal of the federal assault-weapons ban.