The droppings could probably be vacuumed up. The urine, however, will have soaked into the drywall and you just can't wash that stuff. Also, droppings may be embedded into the fiberglass insulation, and urine is likely to have soaked into the paper backing (assuming it's backed), and you're not going to be able to get it out of that, either.
You may be able to get away with patching small areas of drywall where the damage is obvious, but if the smell from the insulation is wide-spread, I believe your only option is to pull all the insulation out and replace it, which also means pulling down all the drywall in the affected areas.
Additional note: It's possible that some of the urine may have soaked into some less removable materials like joists, studs or top/bottom wall plates. While you've got sections of wall and ceiling open, look for stains on the wood and give anything suspicious a sniff test (yay!). If you do find stained wood, do a search and/or post another question about getting the smells out of the wood and take care of that as best you can before sealing that area back up.
In response to questions in the comments:
The nuclear option (replacing all drywall and insulation) would ensure that you got everything, however, your budget, patience, or SO might not tolerate that.
If it were me, I'd start by identifying where the critters are getting in and fixing that first. Then, and only then, would I start working on remediation of the interior issues.
Based on your series of questions, it appears that the smell is what's triggered this exploration and journey of discovery, so I'd start with the worst areas, replacing only what's most obviously offensive. Give it a week or two to air out (spring/summer, when you can open windows and run fans to get fresh air into the place would be ideal) and use your nose to determine if you've gotten the smells under control. Continue to replace insulation/drywall as necessary.
I wouldn't bother with taping/painting until you're comfortable that anything that's producing enough of a smell to bother you has been replaced. Just hang the raw drywall. Sure the house may not look pretty enough for a little black-tie soiree or a Country Living photo shoot during this time, but that's what it'll take.
Once you're satisfied that the smells have been eradicated, take a little breather (pun intended) and revel in your ability to conquer the critters, then set about all the finishing work.
