I'm frankly surprised how many people are freaking out that Faye took her eyes off of Sam for a second. A) She's proven herself a capable worker when handling dangerous tools. B) It is unreasonable to assume that an apprentice should be under 100% supervision at all times while working. C) We now know that Sam made a conscious choice to do a dumb thing in a manner that Faye hasn't seen before (i.e. the willingness to knowingly put her body at risk, not just accidentally)
I think back to shop class, and working in my parents shop, and Appalachia Service Project (think Habitat for Humanity with church kids), etc. and how many times I was unsupervised with power tools. I was also an accident-prone kid. I once severed the tendon in my thumb with a Leatherman knife because I was trying to cut cable ties with it, a knife my grandfather had given me, and it slipped. My parents never blamed anyone but me for the damage (and rightly so). I had handled knives before, even did a report on knife safety, so it was a conscious level of stupidity, similar to Sam trying to trim her nails with a dremel.
Nails grow back, Jim may freak out a little and it'll cause drama, but it's not enough to shut a company down. Maaaaybe small claims court for the medical costs of a box of band-aides, and a small consideration for emotional trauma, if he really wanted to be a hard-ass about it. I can't even imagine a way (short of infection) for Sam to lose a finger with a grinding bit. It would take a while to abrade your finger off. Plus, Sam has clearly learned that she is, in fact, destructible. I'd say that a grounding from the shop for a while (I like the extension due to considering lying to her dad) coming from both sides (Faye and Jim) should do enough for the lesson to sink in.