You can use the official installation method as described in: https://www.newerth.com/?id=downloads&op=displayDownload&category=1&file=xr_setup-1.0-cl_lin_prod.bin
Bare in mind, using the official installation method you need to take care of installing dependencies yourself.
Otherwise, there is also an unofficial installation method using a flatpak bundle, provided by a player called C.I.A., that should work out of the box: https://gitlab.com/sea-eye-aya/unofficial-savage-xr-flatpak
I have not tried the unofficial installation method myself yet, but it appears to be the go-to way of installing Savage XR on Linux nowadays.
See you ingame!