http://revach.net/article.php?id=1921

Section: Halacha   Category: Tshuvos
Piskei Tshuvos: Can You Unstuff A Toilet On Shabbos With Plunger?
The Shulchan Aruch says (OC 336:9) that if a drainage gutter from the roof is stuffed with grass and straw you may clear it on Shabbos with your feet if no one is watching.  You are fixing it with a Shinui and the Chachomim did not assur this since this can cause a great loss.  The Mishna Brura says that you may only clear aside the blockage so that it doesn't interfere with the water flow but you may not totally remove the blockage.

What about a stuffed toilet, may you use a plunger to clear the blockage?  The Minchas Yitzchok (5:75) and others pasken that a plunger would be permissible since it is very easy to clear with a small push.  Certainly in the case of a toilet where there is an issue of Kavod HaBriyos.  Nevertheless says Minchas Yitzchok it is preferable if you can get a non-Jew or do it with your weaker hand as a Shinui.

Rav Moshe Feinstein in the Igros Moshe (4:73) says that you may only unclog it with a plunger if it is partially stuffed and water can still flow through.  Then it is permissible to use the plunger if it can be cleared with one or two pushes.  However if it totally stuffed then it is considered Maaseh Uman, expert work and is considered Uvda D'Chol.  If there is a great need for Kavod HaBriyos to unstuff it, says Rav Moshe, then you can be Meikil and have a non-Jew unstuff it.

Important Note: We try to convey the Tshuva to the best of our ability. We admit that our understanding may not be accurate. Please also understand that this Tshuva may not be the final word on this topic. One should consult a Rav before drawing any conclusions.