In spectroscopic experiments, data acquisition in multi-dimensional phase space may require long acquisition time, owing to the large phase space volume to be covered. In such a case, the limited time available for data acquisition can be a serious constraint for experiments in which multidimensional spectral data are acquired. Here, taking angle-resolved photoemission spectroscopy (ARPES) as an example, we demonstrate a denoising method that utilizes deep learning as an intelligent way to overcome the constraint. With readily available ARPES data and random generation of training datasets, we successfully trained the denoising neural network without overfitting. The denoising neural network can remove the noise in the data while preserving its intrinsic information. We show that the denoising neural network allows us to perform a similar level of second-derivative and line shape analysis on data taken with two orders of magnitude less acquisition time. The importance of our method lies in its applicability to any multidimensional spectral data that are susceptible to statistical noise.