You could be
surprised
but,
actually, there are two ways to cut rasters in ArcMap.
The
classical technique is the
“raster clip” (“raster
cutting”) tool in ArcToolbox.
This has been the only procedure for a long time.
But
since version 10, you have at your disposal the “Image
Analysis” tool in the standard toolbar. This tool
contains
also
a way to cut out rasters and pictures.
The
main advantage of the images analysis toolbar is that you can
see
the final result before exporting it!
We will discuss both methods,
by cutting a part
of the orthophoto coastline of the IGN with the
municipalities’ boundaries of Pont-Aven.

First method: ArcToolbox: clip Raster tool In ArcToolbox (Data Management> Raster> Raster Processing> Clip), double-click the clip tool.

Fill in the fields:
Input raster (required) this is the raster from which you want to extract a part. We want to cut the raster “2011-1820-6787-OL-RGB-L93.jp2”.
Output range (optional) it’s the boundary of the polygon that you want to extract. You can select specific records in the polygon dataset and the cutting will be done according to this boundary. In our case we have selected the polygon corresponding to the municipality of Pont-Aven.
Check the box “use the entities as input for cutting”. This option indicates ArcMap to use the selected records in the polygons layer. If you do not check the box, all the present polygons are used as cutting boundaries.
Raster Dataset output this is the name of the output (cut raster). Adds an extension for the output (.tif, .img, .jpg, etc.) since it is the extension entered here determines the output raster format.
NoData value (optional) All pixels that are outside the cutting boundary will default a NoData value. When you load the raster, these pixels will not appear. You can give another value to make a change. Run the tool by clicking OK. The output raster will be cut according to the Pont-Aven polygon

Second method: Raster Clip (Image Analysis Toolbar) You have to start by activating the images analysis toolbar (Window -> Image Analysis). The window analysis image will be displayed in ArcMap.

This opens the Image Analysis window.

In the image analysis toolbar, select the raster that you want to extract. Make sure the box is checked and that the layer name is highlighted. If you do not, the clip button will be greyed out.

The Clip button is the first button in the “Processing”
section.
As soon as you press the button, a new (virtual)
layer is added to the legend bar with the result of the cutting.
If
you disable the whole raster in
the caption bar, you can see
the result of the order.

All you have to do now is to save this cut raster: right click on the new virtual layer -> Data -> export data: Choose the location and name of the file you want to save. You can also change the size of cells and the raster format output. Click Save.
This second method
can
also
be used without creating a definitive raster. You
can,
simply, use it to reduce the size of the displayed rasters and
speed up your work.
Once
the virtual layer is created, you
can
delete
the original raster legend window, and work on the subset instead of the
original.
If you have to work with LIDAR data, you’ll love this method!!!