In a move meant to remind and warn U.S. businessmen that trade with Cuba is still illegal, the State Department announced yesterday that it was expelling a Cuban diplomat from this country for trying to persuade American businessmen to violate the U.S. trade embargo.

The department's announcement appeared to be a reflection of the generally hard line the administration has taken toward Cuba's communist government, which Reagan sides have accused of fomenting revolution in Central America.

State Department spokesman William Dyess told reporters that Ricardo Escartin, a first secretary of the Cuban interest section that Havana maintains here through the Czechoslovakian embassy, has been given one week to leave this country.

A spokesman for the Cuban mission here issued a statement in behalf of the Cuban Foreign Ministery "rejecting the false accusations made by the State Department spokesman. They reflect the decision of the U.S. authorities to continue the policy of hostility against Cuba."

Dyess said that an FBI investigation had concluded that Escartin was an intelligence agent who traveled extensively in the United States, had wide contacts with American businessmen and "encouraged covert business relationship" with the government of Cuba. Such unlicensed commercial relationships, Dyess said, are in violation of the Cuban assets control regulations issued under the Trading with the Enemy Act of 1963.

Some of Escartin's U.S. contacts have traveled to Cuba as a result of those meetings, Dyess reported, "and we believe have entered into business arrangements" with the Cuban regime. Dyess said that the FBI investigation was continuing and indicated that prosecution of some Americans could be forthcoming.

Dyess also said that Cuba had been very active in trying to get around the embargo in various ways, including setting up front organizations in third countries that would then trade indirectly for American products.

Some U.S. entrepreneurs knowingly collaborated with these fronts, he said, and some did business with them in ignorance of the Cuban connection. State Department officials said many of these fronts were registered in Panama and that the U.S. Treasury Department had a long list of them.

The officials said there has been an upsurge in the number of U.S. businessmen or lawyers representing U.S. firms calling the department to ask about the status of the embargo and even about ways to circumvent it. Some officials attribute this increase in interest to Escartin's activities and the general line that he allegedly espoused, advising businessmen not to worry about the embargo and suggesting how to get around it.

Actually, though direct U.S. trade with Cuba is illegal, there is a considerable amount of business that is done legally by the subsidiaries of U.S. firms abroad acting under other statutes that were passed in 1975.

Kirby Jones, a former press secretary to former senator George McGovern who is now an international trade promoter, estimates that since 1975 U.S. subsidiaries overseas have done close to $1 billion in trade with Cuba in everything from light bulbs to grain, including major U.S. brand-name items.

Jones noted that travel to Cuba is not illegal, nor is it illegal to talk about future business possibilities on such trips. Since 1975, he says he has personally escorted representatives of about 250 U.S. companies to Cuba, and that many American firms have invited Cuban technicians to the United States for an exchange of views.