How to erase a part of a path without altering the stroke's prior design in Illustrator?

Question

I want to erase a part of a path while maintaining the stroke's original look. My chosen stroke is the first one BELOW [Uniform]. I'm new and just a week in at illustrator. This is my very first logo design. I haven't added the missing parts from the sketch though but it can wait.

As you can see with the sketch, the arrows' targets are the parts I want to erase. For now, I will focus on the bite.

Used the eraser but the stroke adjusted itself, which is the main problem. How can I keep it from adjusting?

I filled the bite with white and used minus front but what is this?!

Also, uniting or joining the paths of the bite makes the stroke go crazy so if I needed to do these for the paths in order to properly use pathfinder, you see its useless. Grouping them did not do much (for me)

I also tried covering the discarded parts with white, but I want a transparent background.

These are my newbie attempts. I am ready to do the pro moves if the masters here so advice. I've searched the web already but it seems like I'm the only one with this problem. All popped up "solutions" shown to me are those using the uniform stroke instead, so basically it didn't help me much.

Answer 1

Select all the strokes of the design, and do Object > Expand Appearance*. This will expand the strokes to outlines with a fill.

Then use the Shape Builder tool Shift+M, and hold down Alt/Option while clicking to delete the pieces you don't want.

Example

*Note: This is destructive and irreversible. So, if you want to change your stroke widths later you may want to keep a copy of the original stroked version before proceeding.

Answer 2

The easiest way is to use Object -> Expand -> Stroke, and then make your changes to the resulting vector shape.

Also, use the shape builder tool for combining and omitting the different pieces. That will give you the result you want. Sometimes the pathfinder tools can be very limited in how they work.