The MIP Data Request web pages allows you to view and navigate through the vocabularies.
The Entity Relationship Diagram provides an overview showing links between the vocabularies.
From the home page you can download all of the vocabularies as a single json file or as a Excel workbook, with one vocabulary per spreadsheet in the workbook.
From the top level page of each vocabulary you can download the vocabulary as a csv, json or xlsx file.
A description of the API can be found on the API docs page