Virginia Democrat Edythe C. Harrison, an acknowledged underdog in her bid to oust Republican Sen. John W. Warner, has slipped further behind the incumbent, according to a poll released today by the Richmond Times-Dispatch.

President Reagan also has widened his previously reported 2-to-1 lead over Democrat Walter F. Mondale in Virginia, the new poll of 892 voters shows.

Warner has a lead of 62 percent to Harrison's 20 percent in the poll, taken between Monday and Thursday. Eighteen per cent of the respondents were listed as undecided. The poll was the latest indication of trouble for Harrison, a former state legislator from Norfolk, who trailed Warner 60 percent to 24 percent in a mid-September poll by the newspaper.

Reagan's strong lead over Mondale has jumped since the previous Times-Dispatch poll, rising from 56 percent to Mondale's 28 percent in September to 61 percent for Reagan even as Mondale slipped to 27 percent. Thirteen percent of those polled were listed as undecided.

Aides to Warner, who is completing his first six-year term, said the poll showed that Harrison's attacks on Warner's record have failed.

"It points up that Virginians don't respond to a negative campaign," said Warner spokesman Peter Loomis. "Mrs. Harrison's personal attacks, her attacks on his integrity, and the pattern of distortion of his record, in my mind, have backfired."

Harrison, 50, who has been hampered by poor fund raising and little support from her party, also has assailed Warner's record on defense issues, support from defense industry political action committees, and his budget votes that she says have contributed to the nation's worsening budget deficits.

Steve Morrison, Harrison's press secretary, said he believed that the poll "seems to be skewed toward Republicans" and that "we think people are going to be voting differently."

Harrison was campaigning in the Roanoke area today and returns for campaign appearances in Portsmouth and Petersburg on Sunday. Warner, who appeared with former president Gerald R. Ford in a day-long GOP fund-raiser across the state Friday, was in Newport News for the launching of a Navy aircraft carrier.

This week, Harrison reported having only $23,000 cash on hand and said she has raised $391,506, which is less than the amount of cash that Warner's campaign has on hand. The senator has raised more than $2 million.

In the presidential campaign, the newpaper poll showed that Reagan trounces Mondale on defense issues. Asked which candidate would "keep our nation militarily strong," 71 percent of the respondents said that Reagan would, while 17 percent named Mondale.

The survey also showed that 58 percent of those interviewed expect their federal taxes to be raised in the coming years.

By a margin of 66 percent to 22 percent, those polled reported that they would prefer having Vice President Bush assume the presidency in an emergency rather than Democratic vice presidential nominee Geraldine Ferraro.