[First: get in the habit of always stating in the original post what Inventor version you're using].
Yes and no... You can break the link to the original part, yes, but you will have simply a dumb solid, no editable features. But you can always add features to a derived part whether or not you break the link: fill in holes, direct edit to modify sizes of features, add holes, cuts, bosses, etc.
Reading between the lines, though, I wonder if you're asking whether you can somehow turn the mirrored part into an independent part with the intact feature tree of the original? The answer is, unfortunately, no. However, one possibility to achieve this is to make a copy of the original part, and then use the Mirror tool to mirror the entire solid (see below). This gives you the mirrored part with all features intact. Then use Replace Component to replace the existing mirrored part with the copied one.

In the end, the method you use depends a great deal on what kind of editing you want to do, and how much in common the two parts will have when you're done.
Feel free to post an example and what you want to do with it and I can make more specific recommendations.
Sam B
Inventor Pro 2019.1.2 | Windows 7 SP1
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