Er, get ZAP to do less? :)
ZAP is not currently designed for limited memory or disk space. Both are relatively cheap and so it is not a priority for us right now.
Try reducing the number of threads used by the spiders and active scanner.
Also try to avoid using browsers, e.g. via the AJAX Spider or DOM XSS scan rule.
That will make it much harder to test modern web apps, but browsers take up a LOT of memory, and I suspect you'll have even less luck getting browser makers to reduce their memory footprints ;)
Cheers,
Simon