Terahertz imaging and spectroscopy is an exciting technology that has the potential to provide insights in medical imaging. Prior research has leveraged statistical inference to classify tissue regions from terahertz images. To date, these approaches have shown that the segmentation problem is challenging for images of fresh tissue and for tumors that have invaded muscular regions. Artificial intelligence, particularly machine learning and deep learning, has been shown to improve performance in some medical imaging challenges. This paper builds on that literature by modifying a set of deep learning approaches to the challenge of classifying tissue regions of images captured by terahertz imaging and spectroscopy of freshly excised murine xenograft tissue. Our approach is to preprocess the images through a wavelet synchronous-squeezed transformation (WSST) to convert time-sequential terahertz data of each THz pixel to a spectrogram. Spectrograms are used as input tensors to a deep convolution neural network for pixel-wise classification. Based on the classification result of each pixel, a cancer tissue segmentation map is achieved. In experimentation, we adopt leave-one-sample-out cross-validation strategy, and evaluate our chosen networks and results using multiple metrics such as accuracy, precision, intersection, and size. The results from this experimentation demonstrate improvement in classification accuracy compared to statistical methods, an improvement to segmentation between muscle and cancerous regions in xenograft tumors, and identify areas to improve the imaging and classification methodology.