Disk space just sits there, it doesn't do anything. It can't slow the server down unless it actually uses it.
I take it you have a performance problem in your server.
If it's a straightforward problem of the hardware being simply insufficient, you still have to figure out which straightforward problem it is.
![Wink Smilie](https://www.unix.com/images/smilies/wink.gif)
Not enough CPU power? Faster CPU or, if the application and hardware supports it, more CPU cores. Not enough disk speed? Faster disks, or more disks RAIDed in a more parallel manner, or reconfigure your filesystem/application to work more optimally. Not enough memory? More memory.
It might
not be a hardware problem for all we know, though. Can you give us more details on what's happening?