The discovery of an indigenous girl's body hanging from a tree in Bororó de Dourados was as grim as it was familiar for Brazil's Guarani-Kaiowá tribe, which has one of the highest suicide rates in the world, according to a new report.

Ahead of World Mental Health Day on Thursday, figures from Survival International suggest that the Guarani-Kaiowá are 34 times more likely to kill themselves than Brazil's national average.

This has prompted warnings that a "silent genocide" is under way.

The community of 31,000 people, mostly based in the south-western state of Mato Grosso do Sul, is plagued by alcoholism, depression, poverty and violence after losing its ancestral lands to ranchers and biofuel farmers.

The problem is decades-old, but Survival says the rate has increased in recent years. Since the start of the century, one suicide has been reported on average almost every week.

Almost all are hangings, with ropes, belts or cloth. Most are young. The latest victim, on Wednesday, whose name has yet to be released, was a 17-year-old girl. Last week, a 16-year-old, in Dourados reserve and a 19-year-old in Amambai reserve killed themselves.

"The principle reason is their lack of land," said Michael Mary Nolan, a US nun and human rights lawyer. "The Guarani people think their relationship with the universe is broken when they are separated from their land. They feel they are a broken people." Many in the community cosmologically interpret their situation as a symptom of the destruction of the world.

As well undermining their spiritual base, the seizure of their land by farmers has disrupted the social structure of the community. Traditionally, disputes between families were settled by one side moving away and starting again in a new territory. But this is no longer possible now that thousands of Guarani are crammed together in camps.

One camp in Dourados now has a murder rate that is more than 50% higher than that of Iraq. The stressful, violent environment is worsened by beatings and assassinations of indigenous leaders who try to reclaim their land from wealthy farmers.

The suicides began among the first generation to grow up on reservations, which the tribes moved into in the 1970s, according to Guarani ethnologist, Tonico Benites.

"With no land to maintain their ancient cultures, the Guarani-Kaiowá feel ashamed and humiliated. Many feel sad, insecure, unstable, scared, hungry and miserable. They have lost their crops and their hope for a better life. They are exploited and enslaved by sugar cane production for alcohol," he said. "These conditions of despair and misery cause the epidemic of violence and suicide among the young."

The authorities have recognised the community is in the midst of suicide epidemic, but the government is criticised for not doing enough to deal with the cause.

Although courts have ordered the authorities to demarcate land for the Guarani, little progress has been made since the 1990s when a small tranche of land was returned to them – and the suicide rate temporarily declined. Now, however, the process has almost ground to a halt and some fear it could slide into reverse because Brazil's Congress is dominated by the powerful "ruralista" lobby of landowners.

Many other indigenous communities in the world, including the Tiwi Islanders in Australia, Khanty herders in Siberia and Inuits in Greenland, have unusually high suicide rates. Anthropologists say this is closely linked to the loss of land, which is often followed by social disintegration and economic dependence on charity and state handouts. The result is often alcoholism inside the community and racism outside, which leaves the young – in one man's words – "stuck somewhere between a past they don't understand and a future that won't accept them".

"Sadly, the Guarani are not a unique case – indigenous peoples worldwide often suffer far higher rates of suicide than the majority population," Survival's director Stephen Corry said in a statement.

"So-called 'progress' often destroys tribal peoples but in this case the solution is clear: demarcate the Guarani's land, before more innocent lives are lost.'"

• This article was amended on 16 October 2013 to correct the name of Michael Mary Nolan, from Mary Nolan as the original said.