Vice President Mondale threw his personal support behind Democratic senatorial candidate Bob Short yesterday and asked labor and liberals here in his home state to "stand together" against their most serious Republican challenge in a dozen years.

Mondale implored the state AFL-CIO convention to endorse Short, whose defeat of Rep. Donald M. Fraser in the primary has split the Democrat-Farmer-Labor Party.

"This fall will decide if Minnesota is a progressive, humane state in the tradition of Hubert Humphrey, or something I've never known before," he told several hundred union delegates.

"Stand together. Don't be divided," the Vice President begged. "I'm asking you to do this for Hubert and, if I may be personal, for me."

Labor federation officials thought the Mondale plea improved Short's chances of receiving the two-thirds vote needed for endorsement at today's final convention session, but were not sure of the outcome.

Representatives of teachers, machinists and public employe unions, still smarting over Short's upset of the labor-and-party-endorsed Fraser three weeks ago, said they would try to stop an endorsement.

Louise Swinden, a teachers union delegate, said, "Before, we might have stopped it, but now I doubt it. Mondale's support is awfully important to people here."

Short and his Republican opponent, David Durenberger, both came before the convention Monday for an exchange of charges that evidently added to many unionists' unease.

Durenberger accused Short of anti-union practices in his trucking, hotel and broadcasting businesses and said Short's proposal for a $100-billion reduction in federal spending "would be a disaster for the needy."

Short, in response, stressed his longtime friendship with Humphrey and said he would "withdraw from the contest and concede" if Durenberger could prove his anti-union charges.

Mondale, making his first home-state appearance since he campaigned for Fraser on the weekend before the Sept. 12 primary, told a press conference that Short would support labor reform bills, the Humphrey-Hawkins "full employment" bill and other legislation "in the Humphrey tradition." As for Short's budget-cutting views, Mondale said, "Bob will find out as a senator . . . that he has to deal with the realities of what is possible."

The DFL executive committee has not formally endorsed Short, because liberal elements of the party are still angry about his self-financed primary campaign, which included an open invitation for Republican crossovers.

The Minnesota chapter of Americans for Democratic Action has endorsed Durenberger, a moderate Republican, over Short, and a large ad in yesterday's Duluth newspaper urged write-in votes for Fraser, who has withheld his own endorsement of Short.