We propose a method to monitor the progress of laser processing using laser speckle patterns. Laser grooving and percussion drilling were performed using femtosecond laser pulses. The speckle patterns from a processing point were monitored with a high-speed camera and analyzed with a deep neural network. The deep neural network enabled us to extract multiple information from the speckle pattern without a need for analytical formulation. The trained neural network was able to predict the ablation depth with an uncertainty of 2 \micron, as well as the material under processing, which will be useful for composite material processing.