entering into a situation of ones

Saw the following question:

The Mordechai holds that if one has a garment missing tzitzis, there is no problem in wearing it on shabbos.  The logic is that there is no issur in putting on a four cornered garment.  Once the garment is on, one becomes obligated to put tzitzis on it, but at that point, since it is shabbos and one cannot tie tzitzis, ones Rachmana patrei.

The first Mishna in Beitza says that if one did not prepare anything to do kiseui ha'dam with, one cannot shecht on Y"T.  Why not apply the Mordechai's logic and say that there is no issur in doing shechita, just once the shechita is done, there is a chiyuv to do kisuei ha'dam; at that point, if one has no dirt prepared that is not muktzah, ones Rachamana patrei? 

What's the difference between these cases?