It's difficult to answer definitively without seeing how art is constructed. However, a Clipping Mask should work well.
I'll assume you're starting with something like this:
An object with multiple strokes and blurs applied. I am guessing here :) I used live type, but it doesn't have to be type. Basically a general set up similar to this. The black ellipse is to show contrast and the page. Clearly the type is white with strokes and blurs applied.
Copy the type and use
Edit > Paste In Front so it stays in the exact same position as the original. Then use
Type > Create Outlines. This should remove all those extra strokes and effects once it's outlined. If not, remove them. You just want standard paths and fills, no extras and no strokes.
Now with that copied, outlined type in place, draw a rectangle that covers all the blurring in the original. You want to make certain all parts of the blurred strokes are enclosed within this rectangle.
Select the Rectangle and use
Object > Arrange > Send Backwards. This should move the rectangle in the stacking order to just behind the copied, outlined, type.
Select the rectangle and the outlined type and choose
Object > Compound Path > Make from the menu. You should have something like this:
I filled it with blue and added a gradient behind it so you can more clearly see the separation and the transparency of the type. However, your resulting object may be white (to match the color of the type) or the same color as the rectangle you drew. It really doesn't matter what color this resulting shape is.
Now, with the compound shape you just made selected, hold the Shift key and select the blurred object/type as well.
Object > Clipping Mask > Make from the menu.
You should end up with something similar to this:
All the blurs in tact but the type/object transparent.