For information on growing raspberries see the following two CSU publications.These publications explain things like biennial canes and other things about raspberries that are important to answer your question.
Stem cuttings are not the easiest way to propagate red raspberries due to the biennial-bearing nature of the stems (canes). However, red raspberries tend to produce suckers from the base of the plants. These suckers can be removed from the mother plant with a sharp shovel or trowel and replanted.
Black and purple raspberries often have long canes that bend over and touch the soil and can form new roots at the tips. You can cover these tips with 2 to 4 inches of soil to encourage rooting. Next spring, the rooted tips can be removed from the mother plant with a sharp shovel or trowel and replanted.
Older raspberry plantings may be infected with virus. Taking root suckers or rooted tips from virus-infected plants will pass the virus on to the new planting. Check your plants for signs of disease (yellowing, spots, wilting) before propagating.
To reduce the chance of virus in a new planting, don't locate the new planting where raspberries, strawberries, tomatoes, peppers, potatoes, eggplants or vining melons or squash. have been growing for at least 4 years.
All raspberries should be fertilized as growth starts in early spring and again in early June. Use 1/3 to 2/3 cups of a high Nitrogen fertilizer (21-0-0) per 10 foot hedgerow of raspberries. Fall bearing raspberries (produce a second crop at tips of that years canes) should be fertilized a 3rd time when the tips of that years canes start to bloom. If you want to apply compost or manure, apply it in late fall or early winter.
Thank you for contacting Ask An Expert at eXtension. If you have further questions contact your local CSU Extension Office in Gunnsion: firstname.lastname@example.org, 970-641-1260, 275 South Spruce Street, Gunnison.