Click 'Environments' at the bottom of this tool. Expand 'General Settings'.
Scroll down to 'Extent' and specify this as the underlying larger raster.
Click OK > specify an output raster > click OK to run the tool. The output raster, such as Poly_Raster_2 is the same size as the underlying raster. The extended extent of Poly_Raster_2 has pixel values of 0. Use this raster to clip the polygon shape from the original raster.
Go to ArcToolbox > Spatial Analyst Tools > Conditional > Set Null.
Specify 'Poly_Raster_2' for Input Conditional Raster.
Specify the raster dataset that is clipped (original raster) for Input False Raster or Constant Value.
Specify an output raster.
For the expression, type 'Value = 1'.
Click OK to run the tool. This tool returns values of the original raster where 'Poly_Raster_2' does not equal zero, and returns 'NoDATA' where it does.