The accused are an Iranian, an Afghan and 30 Saudis, all but one of them from the country's Shiite minority, the New York-based watchdog said.
HRW cited Taha al-Haji, a Saudi lawyer who represented a group of the defendants until March, as saying the men were suddenly brought to trial in February.
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Riyadh regularly accuses Tehran of "interference" in the region, where the two countries support opposite sides of the wars in Yemen and Syria.
Relations worsened when Riyadh cut diplomatic ties with Tehran after demonstrators in Iran burned the Saudi embassy and a consulate to protest the Saudi execution of Shiite cleric Nimr al-Nimr.
HRW described the spy trial as "a mockery of justice" that has violated the basic due process rights of the accused, all of whom except one have been detained since 2013.
"Authorities have not permitted defendants to meet with lawyers or provided all of the court documents necessary to prepare a defence," it said.
HRW said prosecutors are seeking the death penalty against 25 of the 32 accused.
Haji said defence lawyers had asked the court to halt an ongoing local media smear campaign against their clients, which they said would lead to an unfair trial.
The charge sheet includes a number of offences constituting "high treason" but there are also charges "that do not represent recognisable crimes", the watchdog said.
These include "supporting demonstrations," "distorting the reputation of the kingdom," and attempting to "spread the Shia confession" in Saudi Arabia, it said.
"Criminal trials should not be merely legal 'window-dressing' where the verdict has been decided beforehand," Sarah Leah Whitson, Middle East director at HRW, said in the statement.
She added that "being a Shia Muslim should not be a crime, and Saudi courts should stop treating it as such.
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