Former Alexandria mayor Charles E. Beatley ousted incumbent Mayor Frank E. Mann yesterday in a election marked by Beatley's last-minute charges that Mann had allowed the Northern Virginia city to become a "baby Las Vegas."

Republicans, continuing their stong gains in the Virginia suburbs, captured three of the city's six council seats, as voters also rejected a reelection bid by councilwoman Ellen Pickering, an independent.

The result will give Beatley, 62, a Democrat, a fourth term as mayor and the Democrats continued control of the city council by a 4-to-3 margin.

Beatley, who had accused Mann of allowing massage parlors and illegal bingo operations to flourish in the city during his term, said last night that his election was a sign that city voters were ready for a change.

"The people have a lot of common sense; they can tell right from wrong," Beatley said last night as unofficial results showed him defeating Mann by a 2-to-1 margin.

The top three vote-getters in the council race were Republicans. Incumbent Robert L. Calhoun, an attorney, apparently captured the spot of vice mayor, which traditionally goes to the council candidate with the highest vote total. Calhoun was followed by Republicans Margaret B. (Mariee) Inman, an aide to State Sen. Wiley F. Mitchell Jr., and Carlyle C. (Connie) Ring, former chairman of the city school board.

The winning Democrats were incumbent Donald C. Casey and Newcomers Nelson E. Greene Sr., and James P. Moran Jr. Greene, a funeral home director will be the second black to sit on the council. Moran is a Senate budget analyst.

Mann's defeat is the lastest in a series of setback for the so-called "old boy networks" of conservative businessmen who once dominated Alexandria's politics. "I hurt like hell," Mann, a wealthy businessman who was 59 yesterday, said last night.

The election of Beatley, coupled with Mann's and Pickering's defeats, will increase the chances of development of the massive Torpedo Plant complex along the Potomac waterfront, a project both Mann and Pickering had opposed.

The Beatley victory insures the continuity of a City Hall staff headed by city manager Douglas Harman, who originally had been hired by Beatley in 1975, but was frequently criticized by Mann.

Mann blamed his loss on newspaper coverage of the race. "The local papers did a hatchet job on me. Beatley was portrayed with a halo, and I had a pitchfork. I've never been whipped this bad before. I feel wiped out, I'm going fishing," he said.

Beatley greeted his victory with the same calm he showed during the often bitter campaign. His sharpest attack came when he said the city had become a "baby Las Vegas" because of its bingo and massage parlors.

The impressive showing of the Republican party was due "to a good, solid party organization that can elect candidates," said Mitchell, one of the architects of the local party. Concern over increasing property tax assessments also helped the Republicans, Mitchell said.

City Attorney Cyril D. Calley, 47, a Democrat, was elected without opposition to a second three year term.

The contest for mayor of the 12-square-mile city of 119,000 people was between the only two men ever to hold the office since a charter amendment in 1961 established the direct election of the city's chief executive.

Mann, a business consultant and landowner, served as mayor from 1961 to 1967, and was elected again in 1976. Beatley, a retired United Airlines pilot and former civic association leader, served three consecutive terms from 1967 to 1976.

In the often bitter contest, Mann campaigned on a platform of bringing what he called "businesslike efficiency" to the city council. During the last two weeks of the campaign Mann frequently said that, if reelected, he would lower the property tax rate from $1.54 to $1.25 for every $100 if assessed value. However, he never specified what city services he would cut if his proposal, which would eliminate nearly $6 million in revenue from city funds, were enacted.

Beatley began his campaign last February by claiming he would work "harmoniously" with the six other council members, a position that please the city's powerful civic associations, who had supported him in the past. A slow and lasonic public speaker, Beatley change his tactics in the last week of the campaign. He forcefully blamed Mann's administration for the proliferation of massage parlors and illegal bingo games in the city.

Mann publicly had supported former Commonwealth's Attorney William L. Cowhig after Cowhig was indicted on bribery and gambling charges in connection with bingo games. "(Cowhig was acquitted in two trials, and a third charge was dropped after Cowhig agreed to resign).

In the minds of many voters, Mann himself was the issue. "I don't like his damn baseball team," one woman said yesterday morning after voting in the City Hall precinct. Last year Mann championed the introduction to the city of a minor league baseball team, the Alexandria Dukes, now the Mariners, which received some city funds.

Other voters criticized mann for his involvement in a company that has not paid property taxes on valuable waterfront land it owns, and for offering to sell the city an apartment complex he owns without prior consultation with the city staff.

But others overlooked those issues in favor of Mann's stated interest in cutting the property tax rate, and his opposition to redevelopment of the mammoth Torpedo Plant complex in Old Town.

"I know Mayor Mann doesn't want to jump in with any bad development there," said Natalie Warwick, 18, who voted yesterday for the first time.

In the council race, Greene based his strength in the 20,000-member black community, which has not had a representative on the council since the 1973 retirement of Ira Robinson. Greene, who raised $13,000 nearly twice as much as his closest rival, also had support from the business community, which liked his outspoken interest in development as a method of raising city revenues.

Council incumbents Calhoun, Casey, and Pickering received support from constituents they had directly helped in the past, or from those attracted by the issues each had stressed during the last three years.

Calhoun translated his concern about rising prices into an ordinance limiting any budget increase to a figure consistent with inflation. Casey originally was alone in criticizing bingo games, but was vindicated with the appointment of a special prosecutor and numerous indictments of bingo figures.

Pickering, who sometimes calls herself the "tree lady" because of her interest in parks, was supported by homeowners concerned about the loss of open space in the city.

Incumbents Bora Lamborne and Beverly Beidler did not seek reelection. Councilman Nicholas A. Colasanto was defeated in the Democratic primary last March. The new council takes office July 1. CAPTION: Picture, CHARLES E. BEATLEY. . .wins unprecedented fourth term