2D nanomaterials have long been considered for development of high permeability membranes. However, current processes have yet to yield a viable membrane for practical use due to the lack of scalability and substantial performance improvements over existing membranes. Herein, an ultrathin graphene oxide (GO) membrane with a permeability of 1562 mL h-1 mmHg-1 m-2, two orders of magnitude higher than the existing nanofiltration membranes, and a tight molecular weight cut-off is presented. To build such a membrane, a new process involving self-assembly and optimization of GO nanoplatelet physicochemical properties is developed. The process produces a highly organized mosaic of nanoplatelets enabling ultra-high permeability and selectivity. An adjustable molecular interlinker between the layers enables absolute nanometer-scale size cut-offs. These characteristics promise significant improvements to many nanoparticle and biological separation applications. In this work, the performance of the membrane in blood dialysis scenarios is evaluated. Urea and cytochrome-c sieving coefficients of 0.5 and 0.4 are achieved while retaining 99% of albumin. Hemolysis, complement activation, and coagulation studies exhibit a performance on par or superior to the existing dialysis membrane materials.