The field of image super-resolution (SR) has witnessed extensive neural network designs from CNN to transformer architectures. However, prevailing SR models suffer from prohibitive memory footprint and intensive computations, which limits further deployment on computational-constrained platforms. In this work, we investigate the potential of network pruning for super-resolution to take advantage of off-the-shelf network designs and reduce the underlying computational overhead. Two main challenges remain in applying pruning methods for SR. First, the widely-used filter pruning technique reflects limited granularity and restricted adaptability to diverse network structures. Second, existing pruning methods generally operate upon a pre-trained network for the sparse structure determination, failing to get rid of dense model training in the traditional SR paradigm. To address these challenges, we adopt unstructured pruning with sparse models directly trained from scratch. Specifically, we propose a novel Iterative Soft Shrinkage-Percentage (ISS-P) method by optimizing the sparse structure of a randomly initialized network at each iteration and tweaking unimportant weights with a small amount proportional to the magnitude scale on-the-fly. We observe that the proposed ISS-P could dynamically learn sparse structures adapting to the optimization process and preserve the sparse model's trainability by yielding a more regularized gradient throughput. Experiments on benchmark datasets demonstrate the effectiveness of the proposed ISS-P compared with state-of-the-art methods over diverse network architectures.