Gladioli grow from corms (things like bulbs in the soil). You can't take cuttings. What you can do is dig up the corms at the end of the summer when the leaves have died back. You'll find tiny baby corms on the edges of the parents which you can take off and grow on next year. Save the larger babies, store them over winter and pot up next spring. It will take them at least 2 or 3 years to get to flowering size.
The quickest way to get more gladdies is to buy more corms next spring.

Ah, thanks Beattie. I'll buy some next spring.

Thank you :o)

Most gladdies (the big-flowered hybrid types) are not quite hardy enough to survive a typical winter in Britain, so if that's what you have you'd be best to dig them up in autumn and store them over winter. I've tried leaving them in but not many come back next year.

There are species gladdies like G. byzantinus (G. communis, ssp byzantinus ) that are hardier. In Cornwall that one can naturalise and has the common name "Whistling Jacks". G. nanus is fairly hardy too.

Ok, thanks Beattie. I didn't plant the Gladioli, they've just appeared, in very strange places, places in which it would be strange to plant them. I will take your advice and dig them up, that will also enable me to plant them in more appropriate spots.

Thanks again! :o)