In Didger 3:

You can crop an image in a raster project using the Image | Extract Bitmap Region command. Then you can export it to a new raster file. The Extract Bitmap Region command will loose all georeferencing if the image is calibrated. If you want to retain the georeferencing, you can either re-georeference the extracted portion, or try cropping in a vector project instead. Just go to Edit | Undo New Bitmap to undo the cropping.

If the image is imported into a vector project, you can draw a polygon over the image, select the polygon and use the Image | Clip Image | Current Polygon command to clip the image to the polygon (you can delete the polygon afterwards if you want). Then, go to View | Project Limits and make sure there is a check mark next to "Clip Map Objects During Export". Then you can export the clipped image to a new raster file. Go to Image | Clip Bitmap | Remove All Clipping to remove the clipping and return the full bitmap.

In Didger 4:

There is only one project.  You can use either the Image | Extract Bitmap Region command or the Image | Clip Image | Current Polygon command.  Follow the above instructions for each command.