This study aimed to improve apple slices’ color and drying kinetics by optimizing the hot-air drying process, utilizing machine and deep learning models. Different steam blanching times (30, 60, 90, and 120 s), drying temperatures (50, 55, 60, 65, and 70 °C), and humidity control methods (full humidity removal or temperature–humidity control) were examined. These factors significantly affected the quality of apple slices. 60 s blanching, 60 °C temperature, and full dehumidification represented the optimal drying conditions for apple slices’ dehydration, achieving better drying kinetics and the best color quality. However, the fastest drying process (40 min) was obtained at a 60 °C drying temperature combined with complete dehumidification after 90 s blanching. Furthermore, machine and deep learning models, including backpropagation (BP), convolutional neural network–long short-term memory (CNN-LSTM), temporal convolutional network (TCN), and long short-term memory (LSTM) networks, effectively predicted the moisture content and color variation in apple slices. Among these, LSTM networks demonstrated exceptional predictive performance with an R2 value exceeding 0.98, indicating superior accuracy. This study provides a scientific foundation for optimizing the drying process of apple slices and illustrates the potential application of deep learning in the agricultural processing and engineering fields.