You can use the Xbox dashboard to make a copy of the adventure map file on another device (USB or cloud). Play the file on your hard drive. When you want to play the adventure map over again, it is best if you first delete the already played one on your hard drive and then copy the backup file anew onto your hard drive (again using the Xbox dashboard). Trying to have two copies of the same world/file (even renamed) on the same device has been known to occasionally trigger a bug that arbitrarily deletes or overwrites other worlds.
Xbox dashboard copy: "Xbox Home" - "Settings" - "System" - "Storage" - Select Storage Device the file is saved on (e.g. "Hard Drive") - "Games and Apps" - "Minecraft" - Select Saved Game file (e.g. "New World") - "Copy" - Select storage Device you want to copy the file to. NOTE: BE SURE THAT YOU ARE SIGNED IN USING THE PROFILE THAT CREATED THE SAVED GAME (listed on the right under the file size). Only the profile that created the world can copy or move it (i.e. this copying does not facilitate file sharing with other people/profiles).
That is the only ways that i know of.
Xbox dashboard copy: "Xbox Home" - "Settings" - "System" - "Storage" - Select Storage Device the file is saved on (e.g. "Hard Drive") - "Games and Apps" - "Minecraft" - Select Saved Game file (e.g. "New World") - "Copy" - Select storage Device you want to copy the file to. NOTE: BE SURE THAT YOU ARE SIGNED IN USING THE PROFILE THAT CREATED THE SAVED GAME (listed on the right under the file size). Only the profile that created the world can copy or move it (i.e. this copying does not facilitate file sharing with other people/profiles).