Can using Neti-Pots and putting tap water up your nose kill you?

Apparently, yes. 

Per the NPR article, Second Neti-Pot Death From Amoeba Prompts Tap-Water Warning:

"Drinking water is good to drink, very safe to drink, but not to push up your nose," says Raoult Ratard, state epidemiologist for the Louisiana Department of Health and Hospitals. Two residents of his state have died after using neti pots this year, the first known deaths associated with neti pots. "The first one could have been a fluke," Ratard told Shots. But now that we have a second one, the only explanation is the use of the neti pot."