The political problems of West Germany's ruling Social Democratic Party continued to pile up today when it was announced that West Berlin's mayor for the past 10 years, Klaus Schuetz, will be replaced.

The announcement follows an apparent financial scandal that has engulfed one of Schuetz's longtime associates in the Party.

Although Schuetz is not involved in the recently disclosed financial irregularities of West Berlin Sen. Kurt Neubauer, the mayor becomes West Germany's third mayor Social Demicratic official to have been bumped out of office in recent months, either directly or indirectly, by the taint of corruption in party ranks.

Schuetz, (moreover,) has been in political trouble for several months - largely because of his strong attacks on the government's East German policy.

What brought on today's surprise announcement, however, appeared to be the sudden disclosure yesterday that Sen. Neubauer had apparently failed to turn over to the government more than $20,000 in commission fees he was paid while a director of the Berliner Bank.

In the big West German state of Hesse, investigations into state bank scandals were a major factor in the resignation of state Premier Albert Osswald last fall and his resignation two weeks ago as state Social Democratic Party leader.

The once-popular Social Democratic mayor of Frankfurt, Rudi Arndt, also left office recently under a cloud of charges of improper campaign-fund use and bribery.

In Bonn, the latest problem in Berlin is being viewed as one more step in a chain of disasters that has seen the coalition government of Social Democratic Chancellor Helmut Schmidt stumble from one crisis to another since being returned to power in federal elections last October.

"It's one more nail in the coffin." said a diplomat here, "but probably not the nail that will kill the government."

The collapse of the Schmidt government would still require a pullout of the smaller coalition partner, the Free Democrats.

Nevertheless, it is clear that the Social Democrats - who have also recently lost clear control of the Munich city government because of fighting between the partner's left and right wings - are in serious trouble nationally.

Schmidt also remains under continuing criticism both in and out of the party for what is viewed as his failure to provide stronger leadership.

This week the party was also forced to suspend the rebellious new leader of the extreme left wing of the Young Social Democrats. This move, however, may help Schmidt now, for the mood of the country is predominantly conservative.

Perhaps most important in the prospect that the present coalition will hold together for a while, however, is the widespread view that the leader of the conservative opposition, Helmut Kohl, is not accomplished enough to take advantage of the government's troubles.

Today's announcement in Berlin by the party's general secretary that Schuetz, 50, would be replaced as mayor by West Berlin Sen. Dietrich Stobbe, 39, did not say exactly when Schuetz would step down.

Sen. Neubauer, who, resigned last night, was the fourth Berlin legislator to resign in disgrace since the last city elections in 1975.

The resignation brought immediate demands from the city's Christian Democratic opposition for new selection.

For Schuetz, the episode brings to a close a decade of governing the Allied sector of the divided city - the longest any mayor has governed there.

The mayors job in West Berlin was, at one time, a springboard to higher office. It was from that job, in 1966, that Willy Brandt moved to Bon, first as foreign minister, and then as chancellor.