Picking unseen objects from clutter is a difficult problem because of the variability in objects (shape, size, and material) and occlusion due to clutter. As a result, it becomes difficult for grasping methods to segment the objects properly and they fail to singulate the object to be picked. This may result in grasp failure or picking of multiple objects together in a single attempt. A push-to-move action by the robot will be beneficial to disperse the objects in the workspace and thus assist the grasping and vision algorithm. We propose a disperse and pick method for domain-independent robotic grasping in a highly cluttered heap of objects. The novel contribution of our framework is the introduction of a heuristic clutter removal method that does not require deep learning and can work on unseen objects. At each iteration of the algorithm, the robot either performs a push-to-move action or a grasp action based on the estimated clutter profile. For grasp planning, we present an improved and adaptive version of a recent domain-independent grasping method. The efficacy of the integrated system is demonstrated in simulation as well as in the real-world.