Three groups of Florida vegetable growers yesterday withdrew their petition charging Mexican growers with "dumping" - selling their produce below cost - and thus seriously undercutting the winter vegetable industry.

The petition was withdrawn only hours before the Treasury Department was to act on it and after hasty negotiations between the State and Treasury departments and the Mexican government.

The Florida growers agreed to withdraw their charges after receiving assurances that the United States and Mexico will begin negotiations on imported Mexican produce.

The growers demanded and received a guarantee that if a settlement is not reached by mid-September, they will be allowed to refile their petition and receive a ruling on an expdited basis.

Supporters of both the Florida growers and the Mexican growers agreed privately yesterday that the State Department and administration special trade representatives were anxious to reach a settlement because the Treasury Department was likely to find Mexican growers guilty of "dumping."

Such a ruling would jeopardize U.S.-Mexican relations at a time when the Carter administration is involved in delicate negotiations on Mexican oil and natural gas reserves.

The petition was filed in September under the 1921 Antidumpting Act, which prohibits foreign producers from dumptin their goods in U.S. markets at below-cost prices. The law has never been applied to produce growers, since perishable products often must be sold below cost.

About 2,100 Mexican growers annually export to the United States almost $200 million worht of tomatoes, peppers, cucumbers, squash and eggplant.

A ruling that Mexico is selling its produce below cost could result in an antidumpint duty to make up the difference. Such a ruling could threaten the jobs of some of the 200,000 Mexicans employed in the produce industry.

The Florida growers said in a statement that they were withdrawing their petition to show that they did not want to monopolize the market, but to coexist with our Mexican brethren."