Contending that Republicans had used "the big lie technique" in a television advertisement on Social Security, Democrats countered yesterday with a commercial of their own and asked TV stations to air it free of charge.

The 30-second Democratic ad features scissors clipping away at a Social Security card; a voice accuses Republicans of repeatedly trying to cut benefits.

"It isn't fair," the voice concludes. "It's Republican."

The ad is the latest escalation of a highly partisan battle between the major parties over the volatile Social Security issue.

It is a direct response to a Republican ad in which a white-haired mailman delivers Social Security checks containing an automatic 7.4 percent cost-of-living increase in benefits.

The checks, the GOP ad claims, show that President Reagan "kept his promise to the American people." Airing around the country, the commercial is part of a $10 million election-year advertising campaign.

The advertisement outraged Democrats. House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) yesterday distributed a "fact sheet" stating that cost-of-living increases are mandated by law and that the Reagan administration has proposed cutting Social Security benefits three times.

Republicans called the Democrats' ad "pure garbage."

"Small children caught with their hand in the cookie jar come up with more believable stories than the Democrats have done in their latest attempt to rewrite history," William Greener, director of communications for the Republican National Committee, said in a prepared statement.

Democratic leaders yesterday said they lacked money to air their commercial, but hoped to raise it. They said state Democratic organizations in Ohio, California and Florida might broadcast the advertisement and urged stations either to refuse to run the GOP ad or provide free time for the Democratic commercial.

"The Democratic Party cannot match dollar for dollar the Republican media buy, nor will it attempt to match them lie for lie," declared Rep. Tony Coelho (D-Calif.), chairman of the Democratic Congressional Campaign Committee. "But if the Republican Party wants this election to be decided by television commercials, so be it."

Opinion polls taken for both parties have found a widespread distrust of Reagan's intentions on Social Security.

Democrats regard it as one of their most promising issues, which the Republican commercial tried to neutralize.

"The Republicans all say they believe in Social Security--a sacred contract with the American people," the Democrats' ad says. "That's what they say. Look at what they do.

"In 1981 they tried to cut cost-of-lving increases by $60 billion over 10 years. In 1982 they said, 'Either increase Social Security taxes or cut $40 billion to help balance the budget.' When are they going to stop? Not until it hurts," the voice-over says.

The GOP commercial has also run into complaints from the U.S. Postal Service, which contends that the use of a mailman represents "an apparent violation" of the U.S. Code and the Hatch Act, which prohibits federal employes from partisan activity.

Vincent R. Sombrotto, president of the National Association of Letter Carriers, has written RNC Chairman Richard Richards that the commercial "deliberately misleads the American public on the attitudes of letter carriers toward President Reagan."