Fruit and vegetable production is increasing worldwide, and farmers currently face a tough challenge in finding enough agricultural workers. Automation of the labour-intensive task of crop harvesting could help fill in this gap between supply and demand. However, picking soft fruits is challenging, as they can be easily damaged if not carefully handled. This paper focuses on designing and evaluating a novel robotic gripper for gently harvesting blackberries, which is nicknamed the Twisting-Tube gripper. The gripper consists of a fabric tube which closes in an enveloping manner due to a motorized twisting action of the ends of the tube. A custom tensile-testing bench was used to test blackberry detachment, release, and damage rates for three types of tubes: radially elastic, fully elastic, and compressible. These tubes were manufactured out of different combinations of foam padding, spandex and food-safe cotton cheesecloth and compared to a handpicked control. The results showed that compressible, thicker cheesecloth outperformed radially elastic or fully elastic or extremely compressible tubes with 82% successful detachment and 95% successful release rates. Furthermore, the Twisting-Tube gripper with thick cheesecloth discoloured at least one drupelet of 19% of the blackberries after 48 hours, which is less than the 33% measured in the handpicked control group, but still more than the 10% of the unhandled berries with discolouration. Moreover, the gripper with thick cheesecloth caused leakage to at least one drupelet for 29% of the successfully harvested blackberries compared to 13% of the hand-harvested control. It can be concluded that the presented Twisting-Tube gripper prototype shows promising results for harvesting small soft fruits.