This is what layers are for. There are twenty of them, which is usually enough for even very complicated projects.
However, since you have separate files, you can append (not import) anything you want from the other file. Generally speaking, you want to append objects rather than meshes. You can make life easier by grouping objects (eg: the back wall, bar, barstools, mirror and shelves with bottles all grouped as “tavern”) and appending entire groups. You can also set up libraries for things like materials.
Cut and paste is a concept that makes sense for 2D applications: paint programs and text editors. In a 3D application like Blender, once you create an object, it’s there. No need to “cut” it in order to “paste” it. You can copy it, duplicate it, mirror it, append it to another file, turn it inside out, whatever you want.
In Blender, you think about datablocks rather than WYSIWYG. Go into the outline view and the OOPS schematic will show you a visual representation of the datablocks you are working with and how they are connected.
Once you get used to the idea of creating and manipulating objects, you’ll find that Blender’s capabilities are much more powerful and useful than mere cut and paste. Which of course, you can also do, as long as you don’t call it “cut and paste” .