Automatic Modulation Recognition (AMR) is a crucial technology in the domains of radar and communications. Traditional AMR approaches assume a closed-set scenario, where unknown samples are forcibly misclassified into known classes, leading to serious consequences for situation awareness and threat assessment. To address this issue, Automatic Modulation Open-set Recognition (AMOSR) defines two tasks as Known Class Classification (KCC) and Unknown Class Identification (UCI). However, AMOSR faces core challenges in terms of inappropriate decision boundaries and sparse feature distributions. To overcome the aforementioned challenges, we propose a Class Information guided Reconstruction (CIR) framework, which leverages reconstruction losses to distinguish known and unknown classes. To enhance distinguishability, we design Class Conditional Vectors (CCVs) to match the latent representations extracted from input samples, achieving perfect reconstruction for known samples while yielding poor results for unknown ones. We also propose a Mutual Information (MI) loss function to ensure reliable matching, with upper and lower bounds of MI derived for tractable optimization and mathematical proofs provided. The mutually beneficial CCVs and MI facilitate the CIR attaining optimal UCI performance without compromising KCC accuracy, especially in scenarios with a higher proportion of unknown classes. Additionally, a denoising module is introduced before reconstruction, enabling the CIR to achieve a significant performance improvement at low SNRs. Experimental results on simulated and measured signals validate the effectiveness and the robustness of the proposed method.