Separate Element
Origami expects a dieline made of one piece. It might contain holes, it might have a complex shape, but it needs to come as one piece, so you can “walk” from any point of the shape to any other point without leaving the paper.
Multiple elements
If the dieline consists of more than one piece, Origami will report one of the pieces as “Separate element”. Here’s a sample dieline made of two pieces:

The two elements above are definitely separate and Origami will only use one of them. The other will be reported.
Unless done on purpose, you will rarely get this error in such a simple way. A more realistic example is below:

Here we have a normal dieline, but its cut lines in the middle are not perfectly connected to the right panel. This mistake effectively separates the right part from the rest of the dieline.
Note: Origami reports such unconnected paths as hanging elements.
Nested elements
Here’s another type of separate elements, the nested one:

This is effectively an O-shaped panel with another square element inside. That element is not connected to the main dieline, and is actually a separate piece inside the hole.
What to do?
First of all you need to decide if the element is separate on purpose or not? If you need a two-piece dieline, you should use multiple scene elements in Origami, each represented by its own dieline.
If this is not on purpose, your best bet is to identify the paths that are not properly connected. Look through the problems list and check all the invalid crease lines and hanging elements reported there. There must be something in the list and once you fix that, the separate element problem will disappear, as well.
Want More Hints?
- Almost Vertical/Horizontal — crease line is probably misaligned;
- Broken Shape — shape is broken apart when folding;
- Path Is Not Closed — the dieline needs a solid, continuous outline path;
- Crease Line In Main Outline — the main outline must be made of cuts;
- Intersecting Curved Cuts — it might not be easy;
- Empty Layout — why there is no dieline visible?
- Hanging Element — what if a path goes nowhere?
- Impossible Crease Line — a crease that shouldn't be;
- Inconsistent Crease Lines — similar crease lines must have same angles;
- Invalid Crease — crease lines have limitations;
- Overlapping Lines — cut and crease lines must not overlap, as well;
- Separate Element — the dieline should come in one piece;
- The Points Are Too Close — avoid crowded spaces;
- Z-Fighting — what to do with overlapping polygons.
There's more from the older folding engines:
- Intersecting Holes — holes must not overlap;
- Impossible Shape — some shapes simply don’t exist;
- Outside Hole — all holes must be inside the outline path;
- Misaligned Elements — ends must meet, perfectly;
- Elements Are Too Small — keep dieline paths simple;
- Triangulation Failed — Origami fails to make a 3D mesh of a dieline.
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