Sometimes it is up to the GM to provide relief from stress created by another group member. The easiest way to deal with it is to allow the other members to talk about it. That talk can save the group from breaking apart, and at the same time build some camaraderie. That talk is also important so the group can figure out a way to stop or at least mitigate the effects of the stressful behavior.
The most common stress type is the one that stems from irritable actions by a group member. These irritable actions will be pointed out to the person by the other individuals in the group in several different ways. Sometimes the individuals will be completely open and honest about it. Other times, the communication is more subtle, taking the form of body language, indirect verbal hints, or even the creation of rules that are squarely directed at controlling the undesirable behavior.
There are cases in which the person will indeed stop their behavior, or at least make an effort to control it. In other cases, however, the person will continue with it leaving the group to deal with the resulting stress.
The easiest way to deal with the resulting stress is to talk about it when the offending person is not present. The goal of the talk is not to help the offender but the group. With that in mind, the GM should allow a considerable amount of freedom to the group. That freedom may entail allowing some of the individuals to make ridiculous imitations, to vituperate the offender, or to dissect the motivations that led to the stressful behavior. That freedom should only the restricted if the individual talking is increasing instead of decreasing the stress of the group.
The key point is to allow everyone their time to talk about that subject. That will allow the individual that is expressing himself to vent his frustrations and at the same time feel the companionship of the other group members.
During that talk, lots of ideas to deal with the behavior will be presented. It is important to listen to them and find the best workable solutions.
Those solutions should be implemented to eliminate or at least mitigate the stressful behavior at the earliest opportunity. Failure to do so may result in the loss of group members, or even in the breakup of the entire group.
Along with everything the GM does in the group, sometimes it is his job to relief the group stress. Talking about it will go a long way to help the situation, but talking can only do so much, when ideas to help with the problem are presented, they should be investigated having the best ones implemented at the first opportunity.