Face anti-spoofing aims to prevent false authentications of face recognition systems by distinguishing whether an image is originated from a human face or a spoof medium. We propose a novel method called Doubly Adversarial Suppression Network (DASN) for domain-agnostic face anti-spoofing; DASN improves the generalization ability to unseen domains by learning to effectively suppress spoof-irrelevant factors (SiFs) (e.g., camera sensors, illuminations). To achieve our goal, we introduce two types of adversarial learning schemes. In the first adversarial learning scheme, multiple SiFs are suppressed by deploying multiple discrimination heads that are trained against an encoder. In the second adversarial learning scheme, each of the discrimination heads is also adversarially trained to suppress a spoof factor, and the group of the secondary spoof classifier and the encoder aims to intensify the spoof factor by overcoming the suppression. We evaluate the proposed method on four public benchmark datasets, and achieve remarkable evaluation results. The results demonstrate the effectiveness of the proposed method.