Dividing Multiple Objects Below With a Stroke

OK.
I made 3 circles one inside the other. each has a stroke applied.
I created 2 triangles and joined them to make an hour glass shape.
I placed the hour glass over the circles.
now i am trying to use the hour glass to cut the 3 circles below. It ends up looking like a spider web.
In these photos the antennae is 2 shapes and on top of the layers that hold what i have descibed. 

In addition to to the method Jacob suggested to hide parts of the paths, if you have a recent version you can alternatively use knockout group by checking this option in the Transparency panel after grouping all and making the objects that you want to act as eraser with 0 opacity. Like with the Opacity Mask method everything is editable directly but without the hassle of releasing and reapplying the mask between edits. This image shows the this.
If you want to actually cut the paths, instead of hiding parts of them, here's one way.
1. select as shown and Cut
2. Paste in Front (now your paths are open)
3. Select All, pick the Shape Builder tool and draw a line as shown to highlight the cutting object/s
4. This is the result from the Shape Builder. Select the cutting path with the black pointer and delete it.
5. Shows the result
click the image to see larger

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    * I merged all three cells on the second row into a single cell.
    * I merged the two right cells on the bottom row, but later, when I moved the cell rule to position the triangular graphic in the inline anchored frame in the right cell, it moved the vertical cell rule in the first row. So, I had to unmerge (or split) the cells, and cut/paste the triangular graphic's anchored frame into the rightmost cell. To position the anchored frame, I moved the vertical cell rule with Shift+Drag, to keep the table width unchanged.
    * I sampled the purple color with the eyedropper tool while cells were selected and the swatch panel was set to fill the selected object.
    * I didn't spend much time matching the type, as you can see. To position the text, I adjusted the cell margins in some cases, and left/right indention in some cases; I'm not sure which is more efficient in situations where there will be different amounts of text to fit. I didn't create cell styles or paragraph styles (BAH! Bad, bad, bad process) because I won't be repeating this stuff, but you probably will benefit greatly from defining styles for your repeating needs.
    * The triangular cut into the bottom row made it easy to manage creating and positioning the graphic. A non-geometrical object might be trickier. The triangle is a text frame, set to negative space above, so it overlaps the cell above it, enough to avoid a black gap.
    * Except for the vertical paper-colored divider line, all the cells have zero-width strokes.
    * I created the table in a text frame, that I fitted down to the size of the table, but I can't remember if I selected, copied, and pasted the text frame into the text flow to anchor it, or if I selected the table in the text frame, copied and pasted it into the flow. Not sure if it makes a difference in work efficiency.
    If I understand your general needs, this should work well for changing text and adjusting the column widths.
    HTH
    Regards,
    Peter Gold
    KnowHow ProServices

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