Mopping is a very integral part of the speedrun, here's an explanation on how it works, and some stats about exactly how fast some methods go.
The rate at which your mop cleans is proportional to how fast it is moving when it registers a hit. If you are moving at full walking speed for every hit (and using the green mop), a puddle will consistently take 7 or 8 hits to mop up. If you instead use the spamclicking method of cleaning a puddle, it will consistently take 10 or 11 or maybe 12 hits to mop up.
In short, don't hold your mop towards the puddle and spam click. Instead, walk back and forth or in a circle while dragging your mop over the puddle. This will clean them about 30% faster. You may also do both at once with no major effect.
Unfortunately, there is a limit on how much speed will boost how fast you clean. I tried using very fast mouse movements to move the mop at lightning speed, but these did not work, and cleaned no faster than walking.
Also of note is that moving back and forth while crawling is slower, so if you're in a tight space, use the spamclick strategy while also crawling around for maximum speed. (unless you're using the yellow mop, but you probably aren't)
If you're interested, i have some further details on exactly how fast each viable mop cleans with different methods of cleaning:
Blue Mop: Walking back and forth: 10-11 hits Spamming: 12-14 hits Crawling back and forth: 14-17 hits Intentionally moving as slowly as possible: 23-25 hits
Green Mop: Walking back and forth: 7-8 hits Spamming: 10-12 hits Crawling back and forth: 14-16 hits Intentionally moving as slowly as possible: 23-25 hits
Yellow Mop: Walking back and forth: 13-14 hits Spamming: 14-17 Crawling back and forth: 13-14 hits (due to speed boost, identical to walking!) Intentionally moving as slowly as possible: 23-25 hits
Since the "intentionally moving as slowly as possible" hit counts are all identical, the "faster" mop is probably not actually faster, it's just that speed boosts the "faster" one more, and boosts the "slower" one less.