The population of the Mediterranean island of Sardinia has made important contributions to genome-wide association studies of traits and diseases. The history of the Sardinian population has also been the focus of much research, and in recent ancient DNA (aDNA) studies, Sardinia has provided unique insight into the peopling of Europe and the spread of agriculture. In this study, we analyze whole-genome sequences of 3,514 Sardinians to address hypotheses regarding the founding of Sardinia and its relation to the peopling of Europe, including examining fine-scale substructure, population size history, and signals of admixture. We find the population of the mountainous Gennargentu region shows elevated genetic isolation with higher levels of ancestry associated with mainland Neolithic farmers and depleted ancestry associated with more recent Bronze Age Steppe migrations on the mainland. Notably, the Gennargentu region also has elevated levels of pre-Neolithic hunter-gatherer ancestry and increased affinity to Basque populations. Further, allele sharing with pre-Neolithic and Neolithic mainland populations is larger on the X chromosome compared to the autosome, providing evidence for a sex-biased demographic history in Sardinia. These results give new insight to the demography of ancestral Sardinians and help further the understanding of sharing of disease risk alleles between Sardinia and mainland populations.