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Grasping in dense clutter is a fundamental skill for autonomous robots. However, the crowdedness and occlusions in the cluttered scenario cause significant difficulties to generate valid grasp poses without collisions, which results in low efficiency and high failure rates. To address these, we present a generic framework called GE-Grasp for robotic motion planning in dense clutter, where we leverage diverse action primitives for occluded object removal and present the generator-evaluator architecture to avoid spatial collisions. Therefore, our GE-Grasp is capable of grasping objects in dense clutter efficiently with promising success rates. Specifically, we define three action primitives: target-oriented grasping for target capturing, pushing, and nontarget-oriented grasping to reduce the crowdedness and occlusions. The generators effectively provide various action candidates referring to the spatial information. Meanwhile, the evaluators assess the selected action primitive candidates, where the optimal action is implemented by the robot. Extensive experiments in simulated and real-world environments show that our approach outperforms the state-of-the-art methods of grasping in clutter with respect to motion efficiency and success rates. Moreover, we achieve comparable performance in the real world as that in the simulation environment, which indicates the strong generalization ability of our GE-Grasp. Supplementary material is available at: https://github.com/CaptainWuDaoKou/GE-Grasp.