What's eating the branches off my plants?

So, I did find a hornworm and got rid of him, but something is literally eating the branches right off some of my plants. Any one have thoughts on what might do this? I live in San Diego, zone 9, so we have squirrels, rabbits, raccoons, and opossums, but no deer. 
 
They are leaving my jalapenos alone, but are eating the yaki blue and bhut jalokia. They don't eat the peppers, just chop off the branches and leave them laying in the dirt.
 
https://i.imgur.com/jQ9hD9z.jpg
 
 
The cut on the branches look quite straight so i'd guess with a rabbit/hare or maybe a marmot... 
 
You sure you don't have a rogue gardener running about?
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Looks like you have rat traps in the background.  I had a terrible problem with rats one year.  To be honest, I wouldn't be surprised if that's what was going on.
 
Anything is possible! I put the rat traps out in the hopes of discouraging whatever critter it is from jumping into the planters. I'm getting a live trap tonight, so I may have some answers in the morning!
 
With my plants, the fucking rats were chewing the branches off, and then defoliating them on the ground.  They were then building nests with their haul.
 
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