You can add actions to a button that happen on click and one of them is 'opengui'.
An error saying 'This gui doesn't exist/is not supported' comes up when trying to open net.minecraft.client.gui.screens.inventory.StonecutterScreen

This menu identifier is the menu info shown when the stonecutter gui is open.

I tried to add it myself by editing menu-identifiers.db but couldn't get it to work.

Will not add this, sorry.