Why does my PSU die everytime I test with multimeter
A multimeter set to measure current (an ammeter) looks like a short circuit, or just a wire. When you connect your multimeter to the PSU, you are overloading it by presenting it with such a low resistance that it can not provide enough current to maintain its designed output voltage, so the protection circuits kick in and turn it off. Were it not for those protection circuits, a fuse in your meter would blow, or some wires would get hot and melt, or something similarly bad would happen.

More likely what you want to do is set your meter to measure voltage. In this mode, the meter looks like an open circuit, as if it's not there at all. Or, if you are interesting in measuring the current being supplied to a load, put the meter in series with the load, not in parallel with it.