Well, it could've been meant to be, but I believe it just makes the most sense. Neither Sauron nor Frodo were just going to let the Ring be pulled off their fingers, so the obvious way to part them would be to bite/slash that finger off. Isildur did it because he was in no position to politely ask Sauron to take off the ring and have tea with him. Gollum bit off Frodo's finger because...well, actually, it's just because he likes fingers, it has nothing to do with the Ring.
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"What mortal feels not awe/Nor trembles at our name,
Hearing our fate-appointed power sublime/Fixed by the eternal law.
For old our office, and our fame,"
-Aeschylus, Song of the Furies
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