Almost twice as many Mexican Americans voted in the Texas governor's race last month as in 1978, and they voted more strongly Democratic than in the past, according to a study by the Southwest Voter Registration Education Project.

But participation by Mexican Americans continues to lag behind that of Anglo voters, the study said. Only about 38 percent of the registered Mexican-American voters in Texas turned out last month, compared with 51 percent of registered non-Hispanics.

Mexican-American turnout in the governor's race increased by 86 percent over 1978, the study said, with an estimated 318,000 Hispanic voters participating, the highest number ever recorded in an off-year election.

Democratic Gov.-elect Mark A. White was the principal beneficiary of the increased participation by Mexican Americans. He captured about 86 percent of the Hispanic vote in his upset victory over Republican Gov. Bill Clements. But the study also showed that White's percentage was the lowest of any Democrat's running statewide.

Clements got 8,700 more Mexican-American votes this year than in 1978, but his percentage fell from19 percent then to just 13 percent this year, the study said. His percentage declined despite a substantial media blitz in south Texas and San Antonio designed to swing historically Democratic Hispanic voters to the GOP.

The poor showing by Clements among Mexican Americans was the most significant development of the election, according to William C. Velasquez, executive director of the Southwest Voter Project.

"In 1980, there was a possibility that the Mexican Americans were swinging toward the Republican Party," Velasquez said. "As a result of this survey, either 1980 was an unusual year or else the Republicans lost an excellent opportunity to make historic inroads into the Mexican-American community."

Velasquez said there is "no question" that more Mexican Americans are voting Democratic now than in the recent past, and he attributed this to the recession and the economic policies of the Reagan administration.

He said other surveys by his group show that where Mexican Americans once listed municipal problems as their chief concerns, they now list unemployment.