A new American tax law designed to reduce spending at conventions abroad is seriously hurting Mexico's vital tourist industry. In less than two months, more than 40 American conventions scheduled to be held in Mexico have canceled their reservations. Tourists officials here estimate the loss at more than $4 million.

The current and likely effects of the law already have caused so much concern here that the Mexican government had launched a diplomatic offensive to obtain special exemption from the law's application for Mexico "as a neighbor" Foreign Ministry sources say the exemption request will rank high on the agenda when President Jose Lopez Portillo visits President Carter this week.

Mexican diplomats and the Minister of Tourism already have called on the State Department for the same reason.

The law, signed by President Ford last October, imposes restrictions on deductions of expenses made at conventions outside the United States. For example: It cuts back per-diem allowances, stipulates air travel must be tourist rather than first-class and requires detailed justification of the number of hours attended and business discussed.

Judging by the letters received at teh convention center here, U.S. organizers mainly object to the huge amount of paperwork generated by the law. "The conventioneers have both told and written me that they don't want to get involved in the red tape, getting witnesses to certify one's attendance, detailed documentation of meetings, etcetera," said Juan Manuel Buendia, the center's director.

"It's like a catastrophe that hit us," Buendia went on. Among sizeable cancelations, the Inland Daily Press Association, for example, annulled its Mexico City meeting of 1,000 members to be held in March, and the Young Presidents' Organization withdrew a get-together for 1,400 executives and their spouses. "There is no doubt about their motives," Buendia added. "They all explain it is because of the new tax law."

Although conventioneers represent less than 10 per cent of Mexico's tourists, their impact on the industry is considered significant. In 1975, for example, the 745 conventions held here - most of them American - brought in 200,421 persons and an income of $55.2 million.

As tourists officials point out, conventioneers are professional people from high-income groups who spend far more on lodging, cultural sidetrips, food and shopping than, say, the thousands of Americans who arrive here in trailers and often bring their own food supply. Moreover, they say, conventions produce a good deal of additional income.

Worried Mexican officials also are approaching their counterparts in Canada, which as the foremost U.S. convetion spot will suffer even more serious effects. "We are going to use all possible means to get exemptions for the two neighbors," one high governement official said. "Our economies are interrelated. Mexico's trade is two-thirds with the U.S., so this law will cut back on our income and therefore on our purchasing power in the U.S."