Consider the climate in which you live when determining the best time to transplant raspberry plants. Early spring is generally the best time to tackle the transplant, as the temperatures are moderate and the plant is dormant. However, if you live in an area that experiences warm temperatures year-round, fall is also a good time to transplant raspberry plants.
The New Mexico State University website recommends carefully severing the roots of the sucker or daughter plants from the mother plant. Use your hands to form a ball of soil around the root system as you move it. However, if the mother plant experienced any sort of disease, remove all traces of soil from the transplant's roots.
Place the raspberry plant into its new location, spreading the roots laterally along the soil at roughly the same depth as the mother plant. Once the plant is in place, spread a firm layer of soil over the top of the roots. Prune the top of the stem to approximately five inches and water the raspberry plant immediately.