With the wide deployment of the Internet of Things (IoT), large volumes of incomplete multiview data that violates data integrity is generated by various applications, which inevitably produces negative impacts on the quality of service of IoT systems. Incomplete multiview clustering (IMC), as an essential technique of data processing, has the potential for mining patterns of incomplete IoT data. However, previous methods utilize notion-strong distances that can only measure differences between distributions at the overlap of data manifolds in fusing complementary information of data for pattern mining. They may suffer from biased estimation and information loss in capturing intrinsic structures of incomplete multiview data. To address these challenges, a semidiscrete multiview optimal transport (SD-MOT) is defined for IMC, which utilizes distances with weak notions to capture intrinsic structures of incomplete multiview data. Specifically, IMC is recast as an equivalent optimal transport between continuous incomplete multiview data and discrete clustering centroids, to avoid the strict assumption on overlap between manifolds in pattern mining. Then, SD-MOT is instantiated as a deep incomplete contrastive clustering network to remedy biased estimation and information loss on intrinsic structures of incomplete multiview data. Afterwards, a variational solution to SD-MOT is derived to effectively train the network parameters for pattern mining. Finally, extensive experiments on four representative incomplete multiview datasets verify the superiority of SD-MOT in comparison with nine baseline methods.