It's a lot easier for people to answer accurately if you don't use confusing and misleading terms. What you're calling a "private server" is just singleplayer mode.
Unfortunately there is no way to copy and paste builds in singleplayer. However, you can run an actual private server, such as MCGalaxy, and then import your save map, and use its /copy and /paste commands to work on your map there.
Read "README.md" to set it up. Then, save your singleplayer world, and put it into the extras/import folder. Then, use /import [levelname]
Then you may use /goto [levelname] to get to it.