One persistent challenge in Speech Emotion Recognition (SER) is the ubiquitous environmental noise, which frequently results in diminished SER performance in practical use. In this paper, we introduce a Two-level Refinement Network, dubbed TRNet, to address this challenge. Specifically, a pre-trained speech enhancement module is employed for front-end noise reduction and noise level estimation. Later, we utilize clean speech spectrograms and their corresponding deep representations as reference signals to refine the spectrogram distortion and representation shift of enhanced speech during model training. Experimental results validate that the proposed TRNet substantially increases the system's robustness in both matched and unmatched noisy environments, without compromising its performance in clean environments.