Democratic presidential hopeful Walter F. Mondale spelled out his policy differences with challenger Sen. John Glenn (D-Ohio) for the first time in the campaign today, and won praise from New York Gov. Mario M. Cuomo (D) for removing "the celluloid images" from the Glenn candidacy.

Cuomo, the influential and uncommitted leader of the second-largest convention delegation, challenged Mondale at a forum here, as he had challenged Glenn in a similar setting Monday, to tell the Democrats where the two leading contenders differed.

Mondale, unlike Glenn, took the bait, ticking off a half dozen differences on economic, defense and arms control policy in as many sentences.

The brief exchange brought the sharpest definition of the differences between the main rivals, just as the Democratic race enters 10 days of important early endorsements by the National Education Association and the AFL-CIO and straw votes in Maine and Iowa.

Cuomo, whose support is a key prize for both Glenn and former vice president Mondale, was the first questioner at a mid-day forum attended by some 700 people, the latest in a series of such sessions the governor has sponsored.

"On Monday in Syracuse," he told Mondale, "I asked Sen. Glenn what in his opinion were the differences on the issues that distinguished his candidacy from yours, and he chose not to answer that question. I put the same question to you."

Mondale began by saying "I have tried to make my campaign as positive as I can, defining specifically what I intend to do as president and how I see this nation's future."

But instead of ending the answer there, as aides said he has on all previous occasions, he went on to say, "There are differences obviously between Sen. Glenn and myself. For example, I strongly supported SALT II and he opposed it." SALT II is the 1979 arms control agreement signed between the Soviet Union and the United States but never ratified.

"I'm opposed to the B1 bomber, and he favors it. I wrote a letter to the Senate earlier this year urging that they turn down poison nerve gas, and he voted for it.

"I believe in real increases in the defense budget, but at a reasonable, manageable pace. The figures he proposes are substantially higher than those I think are supportable."

A Glenn spokesman in Washington said Glenn supported an increase of 6 to 6 1/4 percent after inflation.

Later, in a news conference, Mondale said he supported defense increases "at about the level of the House budget resolution," which was 4.3 percent above inflation, while Glenn, he said, has "cited a figure almost double that."

Next, Mondale said, "I sent several years opposing what was then known as Kemp-Roth a bill for across-the-board tax cuts of 30 percent over three years and opposing the adoption of Reaganomics. I opposed it because I thought it was nuts.

"He Glenn said the other day he voted for" the 1981 Reagan-endorsed three-year, 25 percent across-the-board tax cut "because he thought it would work.

"Finally," Mondale said, "I seek the presidency because I bring . . . a commitment that is deep, life-long and compelling within me . . . to press with all the strength of my heart and mind for social justice in our society . . . , and I would bring to the presidency qualifications and experience that would mark me without exaggeration as the most qualified new president in modern American history."

The answer, like many of the others Mondale gave in the 90-minute forum, was applauded. But more significant to Mondale's future was the praise from Cuomo, the freshman governor who has made it clear in recent interviews he is torn between Glenn and Mondale as the beneficiary of his considerable influence with the big New York delegation.

Again indicating that he would make his choice public in November, Cuomo tantalized Mondale by telling reporters, "If I had a side in this thing, I'd be pleased for him Mondale . I thought he was good on the issues, but it was more significant that Glenn didn't answer the question and this guy did.

"It shows he puts more emphasis on issues and is willing to take on this aura of celebrity and celluloid images and replace them with questions of character and issues."