Protesting farmers, whose tractors continued yesterday to spin playfully around and chew up acres of sod on the Mall, have caused an estimated $2 million worth of damage to the area, according to the U.S. Park Police.

"It could be a couple of million dollars," said U. S. Park Police spokesman George Berklacy. "There's no turf left. It's nonexistent."

While biting cold encouraged 20 more farmers to take their tractors home yesterday, more than 500 of the remaining farmers packed into the Dirksen Office Building and received their warmest official reception of the week from 10 members of the Senate Agriculture Committee.

"We want to hear you and we want to help you," Sen. George McGovern (D-S.D.) told the farmers to thunderous applause. "It doesn't take two thousand tractors in Washington to convince me that you have a real case to put before the American people."

Separately, D.C. police reported their 23rd arrest of the week-long protest. It occurred about 1 p.m. yesterday when a farmer attempted to drive his tractor through the police barricade around the Mall. Two police officers suffered minor injuries, police said. The farmer, Charles M. Witt of Elkton, Tenn., was charged with assault on a police officer and driving under the influence of alcohol.

The farmers, who made a traffic-snarling entrance to Washington on Monday morning, have pulled out 100 of the 625 tractors D.C. police originally boxed in on the Mall and have caused damage that Park Police say is unparalleled by any previous demonstration.

"The entire gravel walkways will have to be replaced," said Berklacy. "There's no question that the damage is considerable."

An official Park Police count shows 55 wooden benches and 57 trash barrels smashed or burned, and numerous traffic signs, 25 trees, two information kiosks and a fire hydrant have been toppled.

The entire Mall will have to be resodded at a cost of nearly $500,000, Berklacy said. There is also possible damage to the waterproof bottom of the Capitol reflecting pool, in which three tractors were driven Tuesday.

A leader of the American Agriculture Movement said the damage was inadvertent. "We didn't request to be put under guard and squeezed up in the Mall," said Gerald McCathern, the movement's "national wagonmaster."

"Those big tractors shouldn't be in that position and our plans originally were to go out of town every night. We have no alternative but to be there."

On the Mall yesterday, Gladys Schroder, a farmer's wife from Baca County, Colo., said the police estimate of damage is wildly inflated for "political purposes."

"They are just makin' that up to get us to leave," said Schroder, who is staying in a large Winnebago near the Capitol reflecting pool. She said she has no intention of leaving.

Berklacy said the final damage estimate would not be known for some time. "We really haven't had an opportunity to evaluate that closely," he said. "You know, the tractors and campers are still there, and that means more damage each day."

The Mall's kiosks appear to be the most expensive single items so far. "These were custom made during the bicentenial and they cost $8,500 apiece," Berklacy said. "You don't repair them, you replace them."

The Park Service spent more than $4 million to redesign the Mall in 1976 and officials estimate the same work would cost 20 percent more today.

"We're going to have to bring the national mall back to the same condition it was in before Monday," Berklacy said. "That's the national front yard."

In the meantime, the Park Service is shelling out $900 a day just to provide the farmers with 16 portable toilets on the mall.

Other costs caused by the demonstration continued to mount. No estimate has been put on overtime costs for city police, but Berklacy said the Park Police were running $50,000 a day in overtime.

City and park police are chartering 34 buses at an estimated $560 a day each to ferry officers to and from the Mall, and 71 more have been hired for the police barricade from Metro's mothball fleet at a one-time cost of about $100 each.

"They were excess buses that we wouldn't be using anyway," said Metro spokesman Cody Pfanstiehl, who emphasized that the rentals had not caused any bus service problems.

Herbert Tucker of the District's Environmental Services Department said trash pickup and other servies were on schedule despite the use of 40 department vehicles for the barricade around the Mall.

Sanding of snow-covered streets is the only service still lagging, he said. Between the farmers, the routine services and the snow, we really got it," he said.

At the hearing yesterday before the Senate Agriculture Committee, six farmers presented their case for one of their top demands, "90 percent parity" that amounts to a return on a farmer's labor and investment that would give him the same relative purchasing power as farmers had in the boom years of 1910-14.

Sen. Edward Zorinsky (D-Neb.), the author of a Senate resolution to give the farmers 90 percent parity, told the farmers that he is saddened by the hard-line reception they've received in Washington from Agriculture Secretary Bob Bergland.

For the second day in a row, Bergland met privately with protesting farmers yesterday and again said that he would not agree to any basic changes in the administration's farm policy.

Earlier, the farmers took about 80 tractors out for a drive around the Capitol. The tractorcade, which was the smallest of the week, lasted for an hour and went without incident.