The way to stop execution is by cancelling the activity. If you are not using activities, then the only way to do this is by altering your automations to periodically check a value that you set off of a button click. This is much harder and requires modifications to your automations. If you invoke them through activities, you can simply cancel the activity.
To cancel an activity, you simply need the ActivityID. This is an integer and is the value returned when you start the activity.
It will stop at the next execution or data point (yellow or blue line I believe it will stop before either, but certainly yellow).
I do not know offhand how to see what is in the queue. I usually just record the ID of each activity to a lookup table as I start them. Then when you wish to cancel, you can iterate through the table and cancel each one. You can also use an interaction and when you start each activity under an interaction, closing that interaction can cancel all running activities.