Why would you skip a team practice at all, especially if you were going to run at that time anyway?
As someone else pointed out, not showing up for summer conditioning might not be grounds for any sort of discipline IF the summer conditioning was outside the dates when your state's high school federation allows practices but that's really beside the point because if the coach wants to toss you for missing an in season practice he probably can do it.
But again, why would you even do that and if you needed to do it, which evidently you didn't, why would you not inform the coach in advance? On the very rare occasions when my kids had to miss a practice we always told the coach well in advance and explained why. I think that only ever happened for practices held during school breaks if we were out of town.
Honestly, there seems no justifiable reason for missing that practice. You need to understand that and make sure anything you say or do about the situation is based on that recognition. Maybe the consequences are more harsh than they should be, I don't know the history here. But all you can do right now, assuming you want to get back on the team, is go to the coach, apologize, accept responsibility for what you did and hope he'll allow you to come back.