You are getting ready to go into battle and you don't want your Wasteland Mutt to get in the way? In the status bar you can press the Stay option and this will make your Wasteland Mutt stay in that spot. To have the dog follow you again press the Follow button that is available in the status bar.
If you would like to put your Wasteland Mutt away for a little while, visit a Stable Manager and park the Wasteland Mutt. When you are ready to take it out again visit a Stable Manager and unpark it or have it towed to your location and unpark.