With the increasing penetration of distributed energy resources (DERs), it is of vital importance to study the dynamic stability of microgrids (MGs) with external control inputs in the electromagnetic transient (EMT) time scale. This requires detailed models of the underlying control structure of MGs and results in a high-order nonlinear MG control system. Higher-level controller design and stability analysis of such high-order systems are usually intractable and computation-costly. To overcome these challenges, this paper proposes a large-signal order reduction (LSOR) method for MGs with considerations of external control inputs and the detailed dynamics of underlying control levels based on singular perturbation theory (SPT). Specially, we innovatively proposed and strictly proved a general stability and accuracy assessment theorem that allows us to analyze the dynamic stability of a full-order nonlinear system by only leveraging its corresponding reduced-order model (ROM) and boundary layer model (BLM). Moreover, this theorem also theoretically provides a set of conditions under which the developed ROM is accurate. Finally, by embedding such a theorem into the SPT, we propose a novel LSOR approach with guaranteed accuracy and stability analysis equivalence. The proposed LSOR method is generic and can be applied to arbitrary dynamic systems. Multiple case studies are conducted on MG systems to show the effectiveness of the proposed approach.