I press F2, it says it saved a screenshot, but doesn't go in the clipboard.

What version of Minecraft is this, and what operating system are you using?
What other mods are you using with this mod?

Windows 10

https://www.curseforge.com/minecraft/modpacks/the-adventures-of-halk

Forge .50

Possible root cause discovered: A mod in the pack runs AWT libraries before Forge creates the mod classes

The bug seems to go away when [SBM] Sheep Metal is removed from the pack, however I can't reproduce it with just Screenshot to Clipboard and [SBM] Sheep Metal, and I can't find any code in that mod to cause a conflict.

Nevermind, I think I found the code that causes this - https://github.com/BuiltBrokenModding/SBM-SheepMetal/blob/master/src/main/java/com/builtbroken/sheepmetal/data/SheepTypes.java. I'll attempt a fix for this as soon as I can.

I've submitted an issue to help resolve this, see BuiltBrokenModding/SBM-SheepMetal#2