General Electric Co.’s troubles came into sharper relief on Tuesday—and the need to salvage the conglomerate took on new urgency—after it revealed federal prosecutors had opened a criminal accounting probe and GE slashed its dividend to a token amount.

By cutting its dividend for the second time in a year, the once-mighty manufacturer can hold on to the little cash it is currently generating. That will buy some breathing room while Larry Culp, its first outsider chief executive officer, restructures the company and finishes...