This article explains how to convert a DXF file with Inkscape in ten steps to an Origin-cuttable SVG.
The DXF file format is a CAD file format that was designed to produce an exact representation of AutoCad DWF files. Although Origin is not designed to accept DXF files, you can use Inkscape to convert some of your two-dimensional data into an SVG file that is cuttable with Origin.
Open your DXF in Inkscape. You can do this either with drag-and-drop or via the menu File > Open
Click OK in the DXF Input screen
Note: it depends on which software was used to generate the DXF. It’s best to read through this article before, as some steps might not be needed. There is also a difference between importing a document via drag-and-drop or the open dialog.
This step is only needed if you imported the DXF via drag-and-drop. Select the document with the selection tool.
Now press CTRL + ⇧ + G or Command + ⇧ + G for ungrouping the file. Sometimes you need to do this more than one time until it looks like in the screenshot below.
Note: For larger documents, this can take a few seconds. This will separate every distinct element in your file, so if you’re importing text, this text may be separated by character, or even parts of inaccurately-rendered characters.
Now remove everything you don't need. Sometimes it is easier to just drag your workpiece out of the frame and then you can delete the rest.
Select the Edit paths by nodes tool 
and select your object twice. You can make this easier by clicking and holding off your objects and dragging a selection box around them.
If selecting nodes this way does not work, and you see only short nodes when hovering over your design with your cursor, you can try the following:
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Select the object with the Selection Tool
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Press CTRL + G or Command + G (sometimes more than once, until it separates in those small objects
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Select all you want to combine to one path by holding down the left mouse button and drawing a frame with the Selection Tool around your object
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Go to Path > Combine
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Now it should appear while hovering over with the Edit paths by nodes tool
as one path -
Go back to the previous step and continue from there
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Press Join selected nodes:
The result should look like this:
Now you can switch back to the Selection Tool . You can group the object for better handling by selecting all parts and pressing CTRL + G or Command + G.
Double-check the size of the object and check your units to confirm that they are what you intend for your project.
Note: Inkscape includes stroke width in its calculation of its bounding boxes. To change this, go to Edit > Preferences > Tools and select Geometric Bounding box. See this article for more tips on Inkscape save settings for use with Origin.
Save your file as a Plain SVG and you're good to go!
Note: If you've converted your DXF to an SVG and Origin still shows an error regarding opening the file, export your SVG in Inkscape as PDF and then re-open the PDF in Inkscape and save it as SVG following the instructions here.