We examine an important combinatorial challenge in clearing clutter using a mobile robot equipped with a manipulator, seeking to compute an optimal  object removal sequence for minimizing the task completion time, assuming that each object is grasped once and then subsequently removed. On the structural side, we establish that such an optimal sequence can be NP-hard to compute, even when no two objects to be removed have any overlap. Then, we construct asymptotically optimal and heuristic algorithms for clutter removal. Employing dynamic programming, our optimal algorithm scales to 40 objects. On the other hand, for random clutter, fast greedy algorithms tend to produce solutions comparable to these generated by the optimal algorithm.