With absolutely no encouragement, red, yellow, and some purple raspberries will produce new plants from root suckers. In the early spring, as soon as the suckers emerge, dig up whole clumps of sucker roots and soil. Separate the roots of the suckers from the mother plant. Then transplant.
Propagating Black Raspberries
Blackcaps and the remaining purples require a different procedure. Give the plants a year or two to get established before prodding them to multiply. In mid-summer, the current season's new canes (or their lateral branches) will be ready for tip-layering: insert the tips of some healthy and actively growing young canes straight down about 4 inches deep into loose, moist soil. Several shoots should emerge in the fall. Early next spring, separate the new plant from its mother and transplant.
This article is a part of our Fruit Gardening Guide for Raspberries.