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In a conversation with a fellow Ancient Greek enthusiast, the name "Medusa" (Μέδουσα, "ruling") came up. I made a rather tortured pun by switching the epsilon to an eta, creating μὴ δοῦσα.

Now, μή is a negative particle, and δοῦσα is a participle from δέω, "bind". I dimly remember using μή, rather than οὐ, with participles. But is this particular construction grammatical? If so, what would it mean?

Draconis
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δοῦσα is a feminine nom. sg. participle, but it's more likely to be taken as the aorist participle of δίδωμι 'give' than the present participle of δέω 'bind': generally, monosyllabic stems (like δε-) don't contract. That said, there are exceptions, and it looks like δοῦσα is actually attested as an alternate of the regular form δέουσα.

μή negates a participle when it has a conditional or general meaning. So μὴ δοῦσα could mean, if taking δοῦσα from δίδωμι, "if she had not given" or "whoever (fem.) did not give"; if taking it from δέω, it could mean "if she were not binding" or "whoever (fem.) does not bind". But note that as brianpck points out in comments, participles don't have absolute tense, so the tense of the translation would vary depending on the main verb and the context.

TKR
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    A minor quibble: the aorist in a participle modifies the "aspect," not the temporality, so it wouldn't necessarily need to be translated by English past or past perfect. – brianpck Dec 17 '18 at 14:42
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    @brianpck True, hence my "could" (I was giving examples to keep things short). I've added an explanatory note. Generally though the tense of participles does line up pretty well with temporality, but relative rather than absolute -- aorist for time prior to the main verb, present for contemporaneous. – TKR Dec 17 '18 at 18:53