Use Css with something like overflow: hidden; and "cut out" what you need.
Use the filter apply_filters('get_avatar', $avatar, $id_or_email, $size, $default, $alt); and override the output of $avatar completely.
The function get_avatar() is pluggable. That means if you hook a plugin function early enough that already defines get_avatar() then this function will be used instead of the core function. See Core (link).