Hi Sunny,
There might be other ways of doing things, but i encourage you to try out a GP tool called "Split Raster" which you can find under the "Data Management Tools - Raster" toolbox. The Split Raster function gives you the ability to clip/extract each individual image parts in your input raster image.
A workflow i would recommend is to 1. create a polygon feature class/dataset, and draw out your regions of interest as individual polygon features. 2. employ split raster function, and select "Polygon features" are your split method. Fill out the remaining tool parameters accordingly.
LMK for your questions. Good luck!