While attempting to create an icon for a side project that I have been working on I was looking for a way to cut away the white lines still present in the final PNG object.

I want to get rid of the white outlines while keeping that space between the objects as a transparent area.

Is the original artwork SVG?

Yes the original artwork is all in SVG

I'd use copies of the stroked (outlined) objects with path-operations to remove the portions of other objects, leaving the gaps.

i.e. 

• Making a copy of the stroked sword into a single object with no stroke (stroke to path, union both created objects).
• Use the new big sword with a difference operation to remove the portion of the lower left delta shape.
• Take the stroke off the original sword and "Inset" its unstroked path to half the stroke width, giving the sword the same size as its original black area.
• Use copies of the crown pieces to make unioned objects to remove the areas of the sword via difference operations.

If that all seems too complicated, you could use the bucket tool on the black areas to make new objects, but that would be pretty ghetto and leave imprecise shapes.

If you share the SVG I can demonstrate.

I'm not exactly sure I entirely follow since I'm pretty new to this program myself, so here's the SVG; hopefully, this helps.

Thank you for the assistance, I'm finally getting back into design after two years and my last program was illustrator so this is all a bit confusing to me as of right now

I'm basically looking for a way to negate white space objects like outlines and other objects from the background elements

Ok, here is a little video of the process.  I usually make short gifs so they can be viewed in the browser, but this is too long and might need to be downloaded, it plays in my browser when I click on the attachment. (10MB)

The three delta shaped objects were groups of two triangle shapes, so those get unioned and combined to a single path object before getting cut.

I use duplicates to union the white stroke to the fill to make a big object and then cut other shapes. Everything gets made into paths. (I had to undo a couple of times because I forgot to make a duplicate.)

There are other ways to do this, but this came to mind first.

Thank you for the video demonstration, I was able to get it fully realized with the help of the process video.

Your help is greatly appreciated!