This paper presents the design, analysis and fabrication of a novel low-cost soft parallel robot for biomedical applications, including bio-micromanipulation devices. The robot consists of two active flexible polymer actuator-based links, which are connected to two rigid links by means of flexible joints. A mathematical model is established between the input voltage to the polymer actuators and the robot's end effector position. The robot has two degrees-of-freedom, making it suitable for handling planar micromanipulation tasks. Moreover, a number of robots can be configured to operate in a cooperative manner for increasing micromanipulation dexterity. Finally, the experimental results demonstrate two main motion modes of the robot.