She asked US President Donald Trump to act quickly on hurricane relief and urged him
to deal with the island's debt crisis.
Yulín Cruz appeared on national TV and called the devastation on Puerto Rico a "humanitarian crisis."
She upbraided acting Homeland Security Secretary Elaine Duke, who described the federal response as "a good news story."
"Dammit, this is not a good news story. This is a 'people are dying' story. It's a life or death story,"
ruz told CNN.
Trump Saturday criticized
Yulín Cruz on Twitter for her "poor leadership ability," saying that the mayor and others in Puerto Rico had been unable to get their workers to help. "They want everything to be done for them when it should be a community effort," the President said.
Yulín Cruz told CNN's Anderson Cooper that Trump's comments -- which she heard about late because of the poor Internet coverage in Puerto Rico -- had made her smile, given what Puerto Ricans were dealing with.
"I smiled. Really, I have no time for small politics or for comments that really don't add to the situation here," she said.
"The truth is staring us in the face. Just today I was telling you we had to evacuate yet another hospital because the generator caught on fire -- so this is another hospital that will not be able to work for another week. We transported 14 patients from one of our facilities."
Yulín Cruz said two entire towns had been evacuated for the first time in her lifetime that she knew of and people were asking their mayors to help.
Asked about Trump's claim that Yulín Cruz had "been told by the Democrats that you must be nasty to Trump," the mayor said: "Maybe he's used to women who have to be told what to do. That's not who we are here in San Juan."
Yulín Cruz said she shared values with the Democratic Party but did not participate in the party and pointed out that Republican Sen. Marco Rubio had sent representatives to Puerto Rico.
"I just think (Trump)'s looking for an excuse for things that are not going well."
Yulín Cruz said she was unsure whether speaking out had been effective but that FEMA had contacted her soon after she gave a media conference Friday to say that more supplies were on the ay.
Bureaucratic red tape was holding up the relief effort she said. "Let's not talk about jurisdiction, head-on collisions, let's talk about how we can make sure that people get stuff fast and easy."
Path to leadership
Yulín Cruz, 54, was born and raised in San Juan, according to a biography
on Puerto Rico's Chamber of Commerce website.
She developed into a leader in high school, where she was an honor student, an accomplished member of the track team and the Student Council president.
Yulín Cruz earned bachelor's degree in political science from Boston University, graduating cum laude, and is a graduate of Carnegie Mellon University in Pittsburgh, where she received a master's degree.
She stayed on the US mainland after her schooling, working in human resources for the US Treasury and in the business world for companies such as Colgate-Palmolive and Cellular One.
After 12 years on the mainland, she moved back to Puerto Rico in 1992 and immediately jumped into local politics. She worked as an adviser to the San Juan mayor and the president of Puerto Rico's House of representatives, according to her biography.
Yulín Cruz became involved in Puerto Rico's Popular Democratic Party in 2003, and was elected president of its women's organization. In 2008, still affiliated with the party, she was elected to the House of Representatives in Puerto Rico.
She ran for San Juan mayor in 2012 against incumbent Jorge Santini and won.
Our Revolution, an American progressive political action organization that backed Yulín Cruz, describes her as "a fierce advocate for the rights of working people, for gender equality and for the rights of the LGBTT community."
"A firm believer that 'the power is in the streets' Yulin strives to seek alliances to empower people and ensure an agenda of prosperity and social justice," the group wrote.
CLARIFICATION: This story has been updated throughout to reflect the full last name of San Juan Mayor Carmen Yulín Cruz.