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You can cut hair with scissors in stages (look at the picture in Post-printing section). Or you can cut it with a knife with long blade (utility knife). Make sure it is sharp.
But it looks like the hair is not adhering properly to the lion body. Check your bridging settings. And if you are using Slic3r there is option "detect thin walls". Change that setting and see if it is better. You can also try Harry_Lion_small.STL, so you don't waste too much filament.