My tales sometimes sometimes remind me of the "Energizer Bunny." They keep going and going. I have a heck of a time deleting parts. I can usually delete a word or two here and there but once I write it, I seldom delete a passage. Some of my short stories are close to novellas in length. Right now I am working on a tale I'm calling "A Dozen Dead Yankee Soldiers." It started out as a short story but ten thousand words later, I still have a long way to go and I can't see where I should delete more than an occasional word. I am beginning to think it is too big for a short story. Chances are, I would have shortened it if I had been writing it on a type writer or in long hand.
It sounds to me like you should be writing novels, and not short stories. Seems like the words flow easily for you and I think you should run with it. Also, I like the title of that story, Yankee that I am.
Start cutting out side plots and unnecessary complications. In short stories, you have to remain focused and disciplined.
Cut out the boring parts. I find a lot of short stories I critique seem to start a thousand words too early and most of the intro could be removed. Similarly, many have people walking into a room, saying 'hello, how are you', 'fine', 'me too' to some other character, then having a conversation and saying 'well, got to go, see you later', 'sure, sounds good', 'goodbye', 'bye' at the end before they walk out of the room. Even if the conversation is important to the story, they could cut a few hundred words from the start and end of the scene by removing all that boring stuff.
It seems like you're one of those people who likes to edit after everything is done. So I say finish the story/novel and worry about editing later.
I think this depends on why you are determined to keep it a short story. Is it for a contest or class or something that has a word limit or is otherwise requiring you to submit something that can be called a 'short story?' If it's not due to some external length constraint, go ahead and finish the story until it is complete. Then go back through and see if there are sidelines or extraneous scenes that can or should be removed. If not, then your story may just be a novel or novella, which is okay. If it is because you are required to keep your story to a short story length, I'm tempted to say you should still finish it as you deem creatively fit, and then go back and see what you might be able to cut out or knock down. If you really can't find anything, maybe you should write a separate short story based on one portion of the story or one character. Maybe you could take one of the characters and put him in a completely different situation from your story, but see how he reacts in this different scenario for your short story. If that doesn't work, you might want to consider keeping your story as a novel or novella that you wrote, but completely start over and write a completely different short story for the contest or class.
I would wait until your finished and see what you have. Then start from the ending and work your way back. Where does your rising action begin?
Chicagoliz said it. If you're writing a short story with constraints then you have to find the things that don't propel the story forward and edit them out (don't delete them, keep them on your hard drive and you may be able to use them another time.) If you're writing a short story for yourself without constraints then let yourself write the full story and think about publishing it as a longer piece.
The "Yankee Soldiers" in my story aren't exactly "Soldiers." This paragraph from the second chapter explains the term. The narrator in this instance is the sheriff of Itawamba County, Mississippi. "Old Carson lay on his right side on the porch. The front yard was littered with blue Busch beer cans, 'Yankee Soldiers' to Carson and many of the beer drinkers in Itawamba County and most other rural areas of the 'real' old South. Most of these Yankee Soldiers had neat .44 caliber holes punched through and through. Surely this was the source of Miz Agnes’s gun shots. Carson must have saved the last round for himself, I thought."