Knowledge Graph (KG)-to-Text Generation has seen recent improvements in generating fluent and informative sentences which describe a given KG. As KGs are widespread across multiple domains and contain important entity-relation information, and as text simplification aims to reduce the complexity of a text while preserving the meaning of the original text, we propose KGSimple, a novel approach to unsupervised text simplification which infuses KG-established techniques in order to construct a simplified KG path and generate a concise text which preserves the original input's meaning. Through an iterative and sampling KG-first approach, our model is capable of simplifying text when starting from a KG by learning to keep important information while harnessing KG-to-text generation to output fluent and descriptive sentences. We evaluate various settings of the KGSimple model on currently-available KG-to-text datasets, demonstrating its effectiveness compared to unsupervised text simplification models which start with a given complex text. Our code is available on GitHub.