Experimentally, vacancy defects are commonly observed in BN nanosheets, expecially nitrogen-terminated triangular defects. Based on first-principles calculations, we systematically investigate the magnetic and electronic properties of BN nanosheets with these triangular vacancies (referred to as Vi(i = 1 − 4) defects with i representing the number of N atoms on each side of the triangle). It is found that the Vi defects bring diverse magnetic states into BN sheets, which are ferrimagnetic for V1, nonmagnetic for V2, ferrimagnetic for V3 and antiferromagnetic for V4 defects. When the isotropic strains are applied, the ferrimagnetic state is sustained for V1 defect, whereas the V2 defect undergoes a nonmagnetic to antiferromagnetic transition and the V3, V4 defects experience an abrupt change in the absolute magnetic moments under small strains, which are originated from the N–N bond breaking at these defects. Different from the BN nanoribbons, the antiparallel coupling is more favorable for the N atoms at the edges of triangular defects. Due to the triangular defects, the band gaps of BN sheets are reduced substantially, which could be further modulated by the strains. When the defective BN sheets serve as a substrate for graphene, the V1, V3 and V4 defects in BN would induce p-type doping in the graphene sheet. Interestingly, when the V2 defect is embedded in BN sheets, the doping behavior of graphene can be well-controlled by the strain, which is charge neutral at the strain-free state and p-type doped under strains. Our studies demonstrate that the rich magnetic and electronic properties of BN sheets with triangular defects enable the system's potential applications in nanodevices.