If you just need a contour cut path it's a lot simpler than what I'm explaining here, but if you need each color of the effect as its own shape for cutting vinyl here is how to do it.
When you have multiple style layers like that, illustrator will just create separate groups from each style layer.. from there you would need to use your pathfinder to drop the top style layer out of the one below it... I'll make a tutorial here.. sorry, but the forum resized my pictures.
Once you've created your style it will appear in the Layers and Appearance panels like this.. You see it's still only one object in the Layers panel, and then all the other attributes are in the appearance panel. This is great for any printing work and keeps you organized, but no good for cut vinyl and the layers it creates on export aren't always pretty.
If we want to simplify this down to the most minimal object we can, it takes a few steps. First we EXPAND the object (With the object select, go to the Object Menu and click the Expand option). Your appearance panel has been set back to normal but you now have some new groups in your layers panel.
You need to remove the top white layer from the middle inner shadow layer in order. The simplest way is to first make each group a compound path... Select the group and hit CTRL+8 (or Object > Compound Path > Make). Notice that once it became a compound object it went transparent (it lost its appearance). Make sure to create a swatch so you can quickly reapply its color.
After both of these groups have been turned in to compound paths, we will use the Pathfinder tool to "remove" the top layer from the bottom layer.
Now that you've subtracted the top layer from the one below, you end up with just those inner shadows we were looking for, but they are a group..
I like to keep my layers as simple as possible.. I've turned all four layers that make up the word in to compound paths, and reapplied color if they dropped their styles. We went from several complicated groups to just three compound paths. One for the inner shadow, one for the white text, and one for the drop shadow.
I think that covers it.. You can do all of these steps while you're working on something if you need files that simple, but keeping all of this style work in the appearance panel allows you the flexibility of making adjustments to it without destroying the shapes. Also, since it's an appearance you can simply create a graphic style from it and apply it to several objects.
There may be a way to take all of these steps and convert them in to an Action, but I've not needed to do that. If something has to be cut from vinyl I will usually just create it in SignLab.
