How to Remove Client Headers in Nginx before passing request to upstream server?

The proxy_set_header HEADER "" does exactly what you expect. See https://nginx.org/en/docs/http/ngx_http_proxy_module.html#proxy_set_header.

If the value of a header field is an empty string then this field will not be passed to a proxied server:

proxy_set_header Accept-Encoding "";

I have just confirmed this is working as documented, I used Nginx v1.12.