Troiano discussed the controversial issue on the Dom Giordano show on 1210 WPHT Monday morning.
"(The song) will continue to play in Wildwood," the mayor said.
The mayor's statements come amid allegations of racism against the 1930s star with a popular recording of "God Bless America."
On Friday, the Philadelphia Flyers said Smith's "God Bless America" recording had been removed from their library, following baseball's New York Yankees.
And by Sunday, the Flyers also removed a statue of Smith outside of Wells Fargo Center.
Smith's connection with the Flyers started in 1969 when a team executive ordered her version of "God Bless America" to be played instead of "The Star Spangled Banner." That led to her performing the song several times before games in the 1970s. A year after her 1986 death, the team erected the statue.
The Wildwood mayor says everyone's quick to be offended.
"What we don't like we're just going to erase. And it's whoever is offended at that time is the one that's pushing the issues," said Troiano.
On Monday night, Action News tracked down the mayor who turned down an on camera interview. He said that he plans to talk to his cabinet to make sure they all feel as passionate about the issue as he does.
Meanwhile, petitions to keep the song have been circulating online.