I'm trying to clear out some of the paper clutter in our house, but our renters insurance requires proof of how much we paid for big ticket items, and some of our warranties are based on when we bought items (noted on the receipts). If I scan all the receipts and warranty information, can I get rid of the originals or will I still need to keep those? I'm thinking if an item breaks and I need to use the warranty or if we need to make a claim against our insurance, will the scans be enough to make a claim?

It should work fine for insurance purposes. And probably for the warranties too, but you should read the warranties to be sure.