Creating a distressed look in vector

Select the object you will distress. If it is text, convert it to curves.
Hold shift and double click the rectangle tool to create a rectangle over the object
Select a suitable texture fill. The fill will determine what portions of the object will get knocked out.
Using the interactive fill tool, adjust the size of the pattern. The size, aspect ratio and angle of the fill will determine what is knocked out. Again, feel free to experiment.
Convert to RGB bitmap. 300 dpi was used above.
Change the mode of the bitmap to black and white. Choose line art as the conversion method. Note that the white colour will be kept, and the black knocked out. Increasing the amount of black will have a heavier distressed look.
Trace the bitmap using logo. You may need to increase the detail to maximum.
Hold control and click on a white portion of the trace results. This will select only the white object in the group (or you can use the object manager). Delete the white portion. If your bitmap still exists after the trace, delete it as well.
You should now have two objects, the original object on the bottom, and the traced result on top. Select both objects and in the property bar press the "Back minus front" to cut the distressed portion.

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