I want to add that white lines on the project, but don't want that line to be visible on the printed element. How can I do that? Working in CMYK in Adobe CS6.
In Illustrator, keep your die lines in a separate layer. You can set that layer to non-print in the Layer Options dialog (double click on the layer).
Checking the Template box will also make it a non-print layer:
When you go to print, make sure that Visible & Printable Layers is selected for Print Layers.
Use overprint on stroke
You simply set that line to "Overprint" in the "Attribute" panel of Illustrator. This way that line will not affect any other CMYK or spot separation and will not be "trapped."
Also, use a spot color on that stroke and rename it
That white line should also be a "spot color" and you should rename that spot color "dieline"; this way the printer will clearly see you have an extra dieline added to your artwork.
Double-click on your color swatch to set the color as spot colors and rename it.
And yes you can put that dieline on a separate layer that has the "print" unchecked as JohnB mentioned.
The simple way to achieve that, use the white line as a guide instead of stroke. To make the stroke as a guide, just select the stroke & press CTRL + 5. At default, guide will be locked in the art-board. To unlock/lock the guide press Atl + Ctrl + ;. This process is very useful for offset printing.