The reliability of disc cutters has a significant influence on the safety and working efficiency of tunnel boring machines (TBMs). To investigate the reliability of disc cutters under different geological and operational conditions, we conducted a series of novel rolling cutting tests on intact and jointed sandstone blocks using different dip angles and interlayers. Different normal forces and rotational speeds of the cutterhead were also applied during the experiment. A novel reliability estimation method, based on a logistic regression model, was then proposed, and the influence of dip angle, strata, normal force, and rotational speed on the reliability of the disc cutter were analyzed. The reliability estimation method consisted of data acquisition regarding the normal force and cutter wear, feature extraction using wavelet packet transform and correlation analysis, and the estimation of the logistic regression model. To obtain the spectrum and normalized wavelet energy for each frequency band, we decomposed the time domain of the normal force by the wavelet packet transform. A correlation analysis was employed to determine the feature frequency bands that were sensitive to wear loss. On the basis of salient feature parameters and wear loss, the logistic regression model was established to evaluate the reliability of disc cutters. The analytical results indicated that the optimal dip angle for rock cutting was 30°. In the presence of mixed-face and single ground, the reliability of disc cutters was primarily affected by the difficulty of TBM excavation and wear loss, respectively. An increase in normal force and rotational speed aggravated wear on the cutter, thus reducing reliability. Furthermore, compared with Rabinowicz's formula, the proposed method considers various geological and operational conditions, making the proposed method more applicable to estimate the reliability of disc cutters.