If you have removed unnecessary files (check /Library/Caches/ on the Mac that sometimes could have a lot of old cached content), and you still don’t have enough space, there’s maybe applications that have installed lots of content into the hard disk. As an example, Apple Loops are placed into /Library/Audio/Apple Loops/. Another place good to check out is /Library/Application Support/.
Now, unfortunately various applications assume that they could find content in the pre-defined places, so you can’t just move it to another disk. What you could do is either to make an Alias (Make Alias in the Finder File menu, or Command-L) or if that does not help, make a symbolic link via the command line tool. The alias should be made on a folder on the other disk, and then renamed so it’s the same as the original folder on the system disk is named. This is where it’s good to first rename the original folder, copy over everything to a new location, make an alias, and then drag the alias back to the original position and give it the same name as the original file. If all that works, then remove the original folder.
Now, it all depends if the application could resolve aliases. There are some programs that due to bad programming or otherwise can’t resolve aliases. In this case you need to make a symbolic link in the command line tool (The command line is in the /Applications/Utilities folder).
As before, copy over the contents to the new location, rename the original file, then in the command line type in something like:
$ ln -s /Volumes/OtherDisk/Folder '/Library/Application Support/OriginalFolderName'
You have to use the ‘ ‘ notation if the folder has a space in the name. The -s option tells that this is a symbolic link so it works across multiple volumes (disks). The /Volumes directory has all the mounted hard disks, where the disk name is the same as you see in the Finder.
A couple of notes, first practice before you do a critical operation, and always have a backup in place in case something bad happened.