The thickness and continuity of oceanic crust is variable. Slow-spreading ridge segments often contain areas of ‘amagmatic’ or tectonic extension, exposing areas of lower-crust and upper-mantle, and having little or no recent volcanism. These are interspersed with areas of ‘normal’ volcanic crust generated by ‘robust’ magmatic accretion. Tectonic spreading is accommodated by displacement on low-angle extensional detachment faults, forming Oceanic Core Complexes. Although ‘amagmatic’ extension appears to be common at slow spreading rates, little is known about the mechanisms that drive the transition from magmatic spreading. Here, we report results from a detailed study of the Mid-Atlantic Ridge (13°N–14°N) and show, paradoxically, that despite the presence of several Core Complexes, melt production remains similar along the present-day spreading axis, which erupts homogeneous ‘normal’ mid-ocean ridge basalt. However, melt production during formation of the older crust off-axis was derived from substantially lower degrees of melting of a heterogeneous mantle. During this magmatically restricted phase, melt production was limited by source composition. Small volumes of an enriched basalt (M1) were produced, derived from low-fraction melts of enriched compositional heterogeneities embedded in an otherwise compositionally depleted upper-mantle, which, in turn, erupted low-fraction incompatible-element-poor basalts (M2). As a consequence of low magma flux, the crust was thin and insufficient to fully accommodate seafloor spreading. Faulting of this thin crust resulted in the development of detachment faults and the formation of OCCs. Thus, we propose that periods of low melt production, resulting directly from depleted, heterogeneous mantle drives the transition from magmatic to amagmatic spreading.