This paper presents a novel method for multiscale stress-constrained topology optimization of functionally graded cellular structures using level-set based trimmed meshes. During the optimization process, trimmed meshes are created by cutting macro and micro background quadrilateral meshes with the zero-isolines of macro- and micro-level set functions. A clear and explicit boundary conforming mesh can be obtained by using trimmed elements placed at the boundary of the solid domain. A continuous field of the macro-height function over a macro background mesh guarantees a perfect connection between adjacent micro-cellular structures. The maximum von-Mises stresses in micro structures are taken as the representative stresses of macro elements and are then aggregated into a p-norm stress measure.