This study investigates fracture behaviour of sandwich structures with foam core slits. These slits are typically machined in the foam core materials to improve manufacturability but inevitably lead to material discontinuities such as resin-starving regions or voids. Using the phase-field method, which does not require the exact location of crack initiation or the crack path known as a prior, the complex fracture process of sandwich structures with different resin-filling slits in the foam core materials is numerically reproduced. We examine the effective stiffness, the peak force, the displacement at crack initiation, and the dissipated energy during fracture of the sandwich structure under shear loads following the ASTMC273 test standard. It is found that the sandwich structure with fully or partly resin filled slits in the foam core exhibits better fracture resistance than the ones with the intact foam and with unfilled slits. The sandwich structure with partly resin filled slits also shows good ductility due to the presence of voids. The effects of the number of slits, slit spacing and foam core density on the load-carrying capacity and fracture resistance are also examined, providing insights into fracture behaviour and damage tolerance of foam core sandwich structures with manufacturing defects.