铲 (chǎn): To shovel or to scoop. This character is found in the word for a shovel, `铲子 (chǎnzi)`. It points directly to the physical act of cleaning.
屎 (shǐ): Poop, feces, or excrement. This is a very direct, informal, and somewhat vulgar character, which adds to the term's humor.
官 (guān): An official, an officer, or a person holding a government post. This character has connotations of high status, responsibility, and formal duty.
The humor and meaning come from the ironic combination of these characters. It creates an oxymoron by assigning a high-status title, 官 (officer), to the very low-status, menial task of 铲屎 (shoveling poop). This elevates the pet to the status of a superior who requires a dedicated “officer” to manage their affairs.