Can you have a blog in a subdirectory hosted on a different server?

A reverse proxy could work, such as varnish or nginx. Using varnish as an example:

backend blog {
   .host = "blog-server-ip";
}

backend default {
   .host = "current-domain-ip";
}

sub vcl_recv {
   if (req.rul ~ "^/blog/") {
      req.backend = blog;
   }
}