I cut back a plumeria a lot so I have lots of branches. I was wondering if
you can get a branch to root that doesn't have a growing end (one having
cuts on both the ends)?

hi jim
most certainly you can!!!
just dry it out for a couple of weeks, as per the usual method ( minimum 2 weeks to form callous) and then pot her up!!
it will take a little longer than a cutting with a growing tip... the roots will form just as quickly as ever... but with no growing tip it will need to push through some new ones from the leaf nodes.
this way you might end up with several branches (i have got 6 new tips from one of these cuttings), rather than just the one or two.
good luck and happy groeing
Renay