It is possible to clip a basemap to reduce the time it takes ArcMap to draw by utilizing the Clip function in the Data Frame properties to temporarily clip data to shape. However, this only visually clips the basemap to display in the map document without actually altering the underlying data. Refer to the following web help for more information: Clipping the Data Frame.
Note: The Data Frame Properties window can be used to set the extent and visibility of an online basemap or layer file for printing or exporting within the map document. Online basemaps or layer files are not acceptable inputs for the Clip tool from the Raster Processing toolset.
The example below shows a specific area on a basemap in the map document:
To clip the basemap to the specific area, follow the steps below: