Here are links to a couple of previous similar questions, with answers FYI -
Depending on how severe the droppings/urine situation is (almost certainly have both, and the urine is usually the larger and harder to clean up issue), some insulation companies will handle modestly contaminated insulation - particularly the companies which use a super vacuum to extract the insulation because that makes it largely hands-free. But you would still need a rodent control contractor probably to do the decontamination of the vapor barrier/ceiling drywall and the framing before putting in new insulation.
Otherwise, for all but heavily contaminated material - many animal/rodent/pest control companies do this sort of thing - commonly removing a gable vent (or creating a hatch opening if no gable vent) to throw the insulation out the end wall into a chute down to a dumpster. Course, have the pest/rodent control contractor seal up the access points the rats were using, too.
For very heavily contaminated material - with a lot of urine contamination - sometimes even a rodent control contractor will not handle it (particuyrarly if the urine is prevalent and strong enough that it mandates hazardous waste protective gear and full-face respirator (as opposed to just fiberglass and dust protection tyvek coveralls and dust mask), then a Biohazard Remediation contractor is occasionally needed - normally only if a large colony (as opposed to a single family) or rodents has been living there recently or currently.
One other thing - if there is electrical runs in the attic, good idea - after the cleanup is done but before theinsulation contractor comes in to put in the new insulation - to have an Electrical contractor check out all the wiring for damage and replace/repair any chewed sections, because there are pretty sure to be some. One of the contractors (maybe the insulation contractor) should also be tasked with checking (after the insulation is all out) for chewed drywall and wood and piping and ducting, to be sure there are no openings from the attic to the house and no damage to venting pipes or ducts.
So - depending on how much a given contractor will take on, sometimes you end up needing a General Contractor to coordinate several subs to perform the different work. With mice and birds they tend not to make too much of a mess (and is commonly just on the surface of the insulation in most areas) and commonly do not chew things too badly - but with rats, squirrels and coons it can be quite messy and a lot of damage.