You can do both. Cut them back and use the trimmings for cuttings. They are perennials, not annuals, in botanical terms. But because they die in cold winters they are, erroneously, called annuals by some in horticulture.

they are called annuals.. up north.. where they cant winter over due to temps ...

if you search out its native range ... its a perennial ...

i would bet my shiny penny.. you used to live up north ... lol ...

you would probably be surprised now many things you think are annuals.. are actually perennial in FL ...

ken

https://duckduckgo.com/?q=coleus+native+range&t=ffcm&ia=web

the second link says:

coleus, is a tropical evergreen tender perennial that has been a popular foliage plant since at least Victorian times.It is native to Southeast Asia and Malaysia.

btw ... i would do both also ... whats to lose.. you might learn something new ...

if you do it in water.. dont let the water roots get too big ... as soon as you see them.. pot them up and grow more roots.. before they go outside ....... and start with smaller pieces ... not those 18 inch pieces ... see link below ...

ken

https://duckduckgo.com/?q=coleus+propagation&t=ffcm&iax=videos&ia=videos

Thank you Floral and Ken! What is weird is that the University of Florida repeatedly calls them annuals. I bought a 6 pack of unnamed at Home Depot last spring and they have performed beautifully. Not much blooming...and people stop and look! They are a winner!

You can also plant a leggy one very deep, or rather bury the stem so that it roots along the length. This will give you a full and robust plant.