Most pure silicone won't stick to itself. Some engineered silicones (like GE's Silicone II product) will stick, although still not as well. But we're not big fans of silicone around here...and I'll leave that at that.
There is a silicone caulk remover out there that works really well. It's called McKanica Silicone Caulk Remover. We've found it at big boxes and hardware stores. We don't make it or sell it, but always recommend it because it does a great job of removing silicone and leaving a good, clean surface for re-caulking. You might try some of that on the stuff you got on the floor.
Hope that helps some. Happy re-caulking!
Charis w/ Sashco - firstname.lastname@example.org