Chiral meta-mirrors provide a unique opportunity for achieving handedness-selective strong light-matter interaction at the nanometer scale. Importantly, the chiral resonances observed in chiral meta-mirrors arise from the spin-dependent resonant cavity which, however, is generally narrowband. In this paper, by exploiting a genetic algorithm (GA) based optimization method, we numerically validate a chiral meta-mirror with octave bandwidth. In particular, in the wavelength range from 1000 to 2000 nm, the proposed chiral meta-mirror strongly absorbs circularly polarized light of one handedness while highly reflecting the other. A field analysis indicates that the observed broadband chiroptical response can be attributed to the multiple chiral resonances supported by the optimized meta-mirror across the band of interest. The observed broadband chiral response confirms the potential of advanced inverse-design approaches for the creation of chiral metadevices with sophisticated functionalities. Based on the Lorentz reciprocity theorem, we show that the proposed meta-mirror can enable chiral-selective broadband second harmonic generation (SHG). Our study indicates that the application of advanced inverse-design approaches can greatly facilitate the development of metadevices with strong chiral response in both the linear and nonlinear regimes.