Can my uncle who lives in a NH in NYC spend down part of his savings to pay for his sister's burial/funeral costs?

Yes my uncle is renewing his Medicaid for long term care at the NH.

To clarify, it is your Uncle who is applying for Medicaid? If yes, your Uncle cannot use his money to pay toward your Mom's or anyone's future funeral expenses. He can use the money to pay for his own pre-paid funeral expenses.

I don't think the SSA rules would accept his spending down on your mom's expenses. She's not a dependent. The money has to benefit the recipient. Check with the Social Security Administration to see what is acceptable.