How do you clear a 2000 Mazda miata 402 code?

You can "cheat" clear it by using a OBDII scanner that allows you to erase it, or simply disconnect the battery and wait for a few minutes.

P0402 is very common for 1999-2000 Miatas. The most common reason is because the engines run very rich and tends to crud up the EGR ports. This is usually fixed by clearing out the Intake Manifold EGR port, and the EGR valve itself:

Cleaning the Intake Manifold Port:

http://miata.net/garage/manifold/index.html

Cleaning the EGR Valve:

http://sites.google.com/site/redcapsmiata/tutorials/egr-valve