Is one allowed to unscrew the top of a sippy cup on Shabbos, the top of the sippy cup containing the straw, dump out the water, put new water in the sippy cup and then screw the top back on, or would this be forbidden because one is thereby making a vessel.
This is an good question if one carefully reads the shulchan aruch 313:6 where the shulchan aruch compares a cup that is in parts to a bed that is made out of parts where the concern is that one will press (shove) the parts in place. The issur would be that one might come to use nails(or similar) and that would be wither מכה בפטיש or בונה (see m.b. 41 there).
Shemiras Shabbos 9:25 learns from the m.b. 313:42 that if the cup has threads that one won't end up pressing the parts in place so it's a non-issue and thus it's mutar.
So yes, a screw on sippy cup is allowed to be unscrewed and re-screwed on shabbos.