Gregor Robertson said Saturday night he's instructed city officials and the chiefs of the fire and police departments to look at how that can be done safely and peacefully.
The 20-year-old woman was found unresponsive in a tent at the site in front of the Vancouver Art Gallery on Saturday afternoon, two days after a man suffered a non-fatal overdose at the encampment.
"There is a serious problem here and we want to address it urgently," Robertson said.
The woman's death is tragic and is also upsetting for him because he has a 20-year-old daughter, he said.
Occupy Vancouver supporters tried to drown him out as he spoke to reporters, with one woman shouting that at least his daughter has a home.
"I think the protest on the really important issues that many of us are passionate about is being undermined by a tent camp and the issues around the right to camp on public space, which is really unfortunate," Robertson said.
"And now we have a critical incident that demonstrates there's life safety at risk here."
Robertson said the city is considering a number of options that include a possible injunction to end the encampment.
Const. Jana McGuinness of the Vancouver Police Department said neither the cause of the woman's death nor her identity are being released as police try to contact her family.
Several people at the protest site said the woman died of a drug overdose and heckled Robertson to provide more funding for addiction services and the homeless.
He told them the city has an outreach worker for the homeless and anyone at the site who doesn't have a home can be accommodated.
McGuinness said police are facing a challenging situation as officials work to try and end the Occupy Vancouver camp.
"Officer safety and the safety of the protesters is paramount as well," she said, adding discussions in the coming days will involve people at the camp.
"We're hoping for co-operation should that time come," she said. "We want it to go smoothly. We don't want to see anybody be hurt."
Last week, the fire department ordered tents to be spaced further apart and for tarps to be removed so they could be accessed in case of an emergency.
But some campers said the orders were merely suggestions and that they didn't have to follow them.
The Occupy Vancouver site has become a major issue in the lead up to this month's civic election as Robertson vies to keep his job amid pressure by his rival to end the occupation at the art gallery.
Lauren Gill, who is running as an independent candidate in the election and is also an organizer at the camp, said the woman apparently died of a drug overdose.
The incident highlights the need for more addiction services because drugs are such a big issue in the city, said Gill, who said she's seen far too many overdose deaths as an outreach worker in mental health and addiction services.
"I think it's an issue that's all over our city and this is why we need Insite," she said of the supervised injection site in the Downtown Eastside where people shoot up their own drugs under medical supervision.
"We just lost a member of our community," she said. "It's a really strong community down here and we're going to do whatever we can to support each other."
Gill said she does not want to turn the death into a political issue and is hoping other candidates don't do that either.
The woman was found dead by a friend at about 4:30 p.m., just before a band called DOA started playing a scheduled gig at the camp.
On Saturday, tensions seem to be growing at the site. One television camera operator was shoved to the ground and some protesters began hassling reporters.