When someone calls me a [“mot insultant”/”gros mot” (disons “con”, par exemple)] in French, they sometimes preface the word with “espèce de.” Usually with only the context/tone of voice/gravity of my transgression I can surmise that being an “espèce de con” is somehow worse than being simply a “con.”

In light of the above discussion of my personal experiences with the “reinforcing nature” of “espèce de” when followed by an insulting word addressed to a person, the suggestions proposed below might seem to be just the opposite of what you seek. However, other meanings/uses of “espèce” and “espèce de” include “comparable/semblable” and “sorte/manière”, without emphasizing/reinforcing the negative.

Therefore, I think that prefacing “juron(s)” (for minced blasphemous oaths) and “gros mot(s)”/”grossièreté(s)” (for minced, non-blasphemous oaths/vulgarities) would accurately capture the notion in French, with a gentle double entendre thrown in for good measure:

“Espèce de juron” = “minced (blasphemous) oath”, e.g., “Sang de bois” pour “sang de dieu”

“Espèce de gros mot”/”Espèce de grossièreté” = “minced (non-blasphemous) oath/vulgarity”,e.g., “mince” pour “merde”

I really tried to work with the French word “mince” to get something, because:

1) as you mention the cooking/chopping sense of “mince” in French is spot-on with its “word” sense in English;

2) “mince” itself, as mentioned above, is a minced (non-blasphemous) oath/vulgarity in French for “merde”; and

3) ‘mince” is close to an antonym for “gros” in French,

all of which leading me to the following:

“gros mot(s) mince(s)”/”gros mot(s) mincé(s)” and even just “mot(s) mince(s)”/”mot(s) mincé(s).”

However, all of these seemed to me to be a bit too “mignon”-sy (except perhaps the last one, “mot(s) mincé(s)”), so I went with “espèce de ….”

You might call it a délicatesse … because its scrupules sur ce qui touche à la probité fits with ‘minced’ oath, and, délicatesse has a soupçon of the “culinary delicacy” (agréable au goût) also.

Alternatively maybe a juronet or juronette, or (following Papa Poule’s line of thinking) “un fils de juron”.

The above are jokes of mine, i.e. neologisms.

In existing usage you can find un adoucissement being used:

De câline, lui même un adoucissement de calice

Or Juron adouci (see here and here) is used — not used very often, but the phrase is descriptive enough that you could understand what it means even without having seen it before.