The purpose of satire is to point out human flaws in a humorous way in order to instruct and possibly change humanity. In this case, the subject of the satire is man's willingness to just do what he is told without questioning it or without making good choices for himself. The play has an overarching theme of existentialism, and that philiosophy of life states that man must choose to act and take actions that are for the betterment of self and/or society. If a person fails to choose and fails to act, then he is considered existentially dead. Just breathing and going along through life with active action is not truly being alive, it is mere existence.
Rosencrantz and Guildenstern are considered existentially dead and Stoppard uses humor to make his point. These men are confused, don't really know why they were called, they only came because they were called in the first place, and even when they seem to be able to make a choice for themselves, they don't-- they let their fate happen to them rather than making a new ending for themselves. In this play, they read the re-write of the letter for England and learn that they will be put death in England, but they don't do anything to stop it. Stoppard is illustrating through this negative example how to live -- live better than these two characters do. Along the way to this message, Stoppard has many jokes at their expense and that is part of the satire as well. One of the most important "jokes" is that the Player seems to know everything about them (because he lives on at the end of Shakespeare's Hamlet) and he taunts them with that throughout the play -- unbeknownst to them even until the last pages. The play uses silly humor/jokes, bawdy humor with the players, and deep philosophical statements all in an effort for the audience to see how to better examine their own lives and how they live them.