Can I sort a list of items based on another list of items?

Yes, it's possible.

<Edited By Host>

The following script seems to do what you are asking for, assuming that every item in petList also belongs to petOrder:

set petList to {"Garfield", "Pluto", "Snoopy"}

set petOrder to {"Snoopy", "Tweety", "Pluto", "Top Cat", "Garfield"}

set newList to {}

repeat with k from 1 to (countpetOrder)

if itemk of petOrder is in petList then copy itemk of petOrder to the end of newList

end repeat

newList--> {"Snoopy", "Pluto", "Garfield"}

My pleasure. Thanks for your feedback.