Can I split a PCB using Altium?
Yes.
It's not really clear what you are asking, but the answer is &quot;yes&quot; because Altium can do anything regarding PCB sizes.
Either...
...you mean that you have an existing design and want to &quot;dice&quot; it. In that case, just use cut/paste, as you would in any other software, to move whole sections of layout into a new PCB document.
Or...
...you mean that you have 4 smaller designs in your head and you want to draft them. In that case, create a separate PCB project for each.
Update: Re: Question Edits
From a pure manufacturing basis two 1 unit x 1 unit designs should never be cheaper than one 1 unit x 2 unit design ceteris paribus and assuming they all fit in one panel (which is almost always the case). If you are encountering cost anomalies with your vendor, contact your vendor and negotiate or switch vendors.
That said, there is no built-in functionality to auto-partition a design in the manner you have suggested because there is an insufficient business case for Altium (or any EDA company) to develop such functionality.
Cut-Paste will work fine, but as others have suggested, it's probably best to leave it as one larger PCB.