The literal translation is to "excrete my bird stomach"
Generally used in a time of frustration rather than words such as "shit" or "fuck". Many use it to express their anger or annoyance as well.
Another interpretation is a sexual pickup line to convince your partner to essentially "poop you out" or in other scenarios, it can be taken in a more sexual context.
That awkward moment when your crush doesn't like you back
"Shiz my gizzard"
That moment you realize you aren't going to pass math
"Shiz my gizzard"
"Hey babe, wanna, wanna.... SHIZ MY GIZZARD?"
"Don't I always?"