Data visualizations are created and shared on the web at an unprecedented speed, raising new needs and questions for processing and analyzing visualizations after they have been generated and digitized. However, existing formalisms focus on operating on a single visualization instead of multiple visualizations, making it challenging to perform analysis tasks such as sorting and clustering visualizations. Through a systematic analysis of previous work, we abstract visualization-related tasks into mathematical operators such as union and propose a design space of visualization operations. We realize the design by developing ComputableViz, a library that supports operations on multiple visualization specifications. To demonstrate its usefulness and extensibility, we present multiple usage scenarios concerning processing and analyzing visualization, such as generating visualization embeddings and automatically making visualizations accessible. We conclude by discussing research opportunities and challenges for managing and exploiting the massive visualizations on the web.