The application of deep learning neural networks enables the processing of extensive volumes of data and often requires dense datasets. In certain domains, researchers encounter challenges related to the scarcity of training data, particularly in marine biology. In addition, many sounds produced by sea mammals are of interest in technical applications, e.g., underwater communication or sonar construction. Thus, generating synthetic biological sounds is an important task for understanding and studying the behavior of various animal species, especially large sea mammals, which demonstrate complex social behavior and can use hydrolocation to navigate underwater. This study is devoted to generating sperm whale vocalizations using a limited sperm whale click dataset. Our approach utilizes an augmentation technique predicated on the transformation of audio sample spectrograms, followed by the employment of the generative adversarial network StyleGAN2-ADA to generate new audio data. The results show that using the chosen augmentation method, namely mixing along the time axis, makes it possible to create fairly similar clicks of sperm whales with a maximum deviation of 2%. The generation of new clicks was reproduced on datasets using selected augmentation approaches with two neural networks: StyleGAN2-ADA and WaveGan. StyleGAN2-ADA, trained on an augmented dataset using the axis mixing approach, showed better results compared to WaveGAN.