I am wondering if anyone knows if there is arcpy functionality available in ArcGIS 10.3 or can be coded easily to replicate the select visible rasters command (manually right clicking on a Mosaic Dataset Footprint in the table of contents in an ArcMap session).

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This is similar: Use ListDataFrames() to get current display extent and then MakeMosaicLayer() to create a temporary mosaic.

import arcpy
mxd = arcpy.mapping.MapDocument("CURRENT")
df = arcpy.mapping.ListDataFrames(mxd, "*")[0]     # grab 1st dataframe in map
#df = arcpy.mapping.ListDataFrames(mxd, "Main")[0] # grab dataframe named 'Main'
    'Orthophotos',  # input mosaic
    'test_mosaic',  # output mosaic
    '#',            # Optional WHERE clause
    df.extent       # clipping box coordinates


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