Actually, it depends.
It depends on what data you want to store on the external vs. internal drive.
If you choose to, essentially, clone your Mac system onto the Mac Mini, then you don't have a lot of control.
However, if you first setup your account on the Mini, and specifically configure the target directories first, before initiating the Time Machine restore, then you may have some option.
For example, if you want to store your home directory on the external drive, boot the new Mini, create your account, and configure the (empty) home directory on the external drive.
Now when you initiate Time Machine, it will restore your home directory data to the external drive, and non-home directory data on the internal drive. Viola!
It can be tricky, though, depending on what level of content division you want. You might find it works for things like you Music library or Photos albums.