Don’t use the more tag to manually define excerpts. There’s a separate input field for that. If it’s not visible, go to “screen options” in the upper right corner of the edit screen to enable it.
What exactly is shown on your single and archive pages depends on your theme. There is no general way to address this. But if you use the excerpt field for what it is meant to do, any decent theme will pick it up and display the excerpt on archive pages and the post (where you have removed the excerpt) on the single page.