This from the internet: "Blackberries can be propagated through leafy stem cuttings as well as root cuttings. If you want to propagate lots of plants, leafy stem cuttings are probably the best way to go. This is usually accomplished while the cane is still firm and succulent. YouâÂÂll want to take about 4-6 inches of the cane stems. These should be placed in a moist peat/sand mix, sticking them in a couple inches deep. Rooting hormone can be used but is not necessary. Mist well and put them in a shady location. Within 3-4 weeks, roots should begin to develop."

The time it would take you to get a fruit crop from these plants would be quicker if you used dug-up suckers from raspberries and tip-rooted growth from blackberries. I assume you have some source of plants that you want to borrow from.

Using the above Internet method could work but could take a year or two longer to get fruit.

Just putting cuttings in water would not likely work.