Graph convolutional networks (GCNs) are becoming increasingly popular as they can process a wide variety of data formats that prior deep neural networks cannot easily support. One key challenge in designing hardware accelerators for GCNs is the vast size and randomness in their data access patterns which greatly reduces the effectiveness of the limited on-chip cache. Aimed at improving the effectiveness of the cache by mitigating the irregular data accesses, prior studies often employ the vertex tiling techniques used in traditional graph processing applications. While being effective at enhancing the cache efficiency, those approaches are often sensitive to the tiling configurations where the optimal setting heavily depends on target input datasets. Furthermore, the existing solutions require manual tuning through trial-and-error or rely on sub-optimal analytical models.In this paper, we propose Slice-and-Forge (SnF), an efficient hardware accelerator for GCNs which greatly improves the effectiveness of the limited on-chip cache. SnF chooses a tiling strategy named feature slicing that splits the features into vertical slices and processes them in the outermost loop of the execution. This particular choice results in a repetition of the identical computational patterns over irregular graph data over multiple rounds. Taking advantage of such repetitions, SnF dynamically tunes its tile size. Our experimental results reveal that SnF can achieve 1.73× higher performance in geomean compared to prior work on multi-engine settings, and 1.46× higher performance in geomean on small scale settings, without the need for off-line analyses.