Mechanicals are known for not having the sharpest blades or having a burr on them. Some are better than others. Just working the blades in and out of the head can dull them.
I have taken the blades out of the heads and used a lansky sharpener to put an edge on them. This is the sharpening device that has a clamp for the blade and the stones are on guide rods so you get the perfect angle every time. I actually have a nock off version, but it works reasonably well.
It's a pain with those little blades, but it does the job. Still not as sharp as replacable fixed heads though.
I don't know of any way you could sharpen the blades in the heads on a mechanical. I'm not sure how sharp the replacable blades are mechanicals, never messed with them. Mechanicals are one shot deals for me. Once I use them I just get new heads. Which is sort of stupid considering how expensive they are. I normally only use one a year though, if I decide to use mechanicals. So 30 bucks or so a year isn't a real big deal. Especially when you consider the price of slugs for my slug gun

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Paul