Choose the "Clip" or "Extract by Mask" function from the Geoprocessing tools, select the raster layer, specify the shapefile as the clipping boundary, and execute the tool to clip the raster image precisely according to the shapefile boundaries.
Neeraj Bohat I think this might work but you have to do an additional step,
you have to convert the data to points and do interpolation, while applying interpolation, you will have to go to the "Environments" tab and, under the "Raster Analysis" you can select the Shapefile that you are using as the "Mask"
The reason of your issue is that the pixel size is such that the shapefile is unable to get information about the boundary layers properly.
you must firstly increase raster resolution by decreasing the raster pixel , secondly, the raster and the shp coordinate system must be the same. for obtaned good result