We can posit the following explanation:
Rashi’s primary aim with his explanation is not (really) to explain the double mention of “Nephilim... from among the Nephilim” in the verse — because first of all, the repetition of “Nephilim” on its own is not (particularly) unusual, for we find many times in Torah that a word is repeated for greater emphasis;
[like the title “a righteous person who is the child of a righteous person,” which highlights the great piety of the child; so too in this context, through saying “Nephilim (giants)... from among the Nephilim,” the verse is further emphasizing {their great stature}, and the Jewish people’s corresponding great fear of them (thus, there is no need to say that each mention of “Nephilim” has its own meaning, with different explanations)],
In addition, if the difficulty in the verse was the double mention of “Nephilim,” then Rashi should have also (and indeed, primarily) cited (in the header of his explanation) the words, “from among the Nephilim,” since these are the extra words!
Instead, the question (that Rashi is addressing) is as follows: The preceding verses record the spies’ description of the strength of the inhabitants of the land, “But, the people... are powerful... the cities... and we also saw there the offspring of the giant.” A question arises: What are the spies adding (when “they brought forth an evil report on the land”) to their previous statements of “and we also saw there the offspring of the giant” (aside from adding the title of “Nephilim”)?
Addressing this, Rashi explains that “Nephilim” means “giants from among the sons of Shamchazai and Azael, who fell from the heavens.” This clarifies how the spies were adding a completely new element: These {Nephilim} were completely different from the “offspring of the giant” mentioned earlier (who were discussed in parshas Bereishis, “the Nephilim were on the earth”). Those were human beings who instilled fear in others simply because of their large, tall stature — they were merely giants. In contrast, the “Nephilim” in this verse are (giants — but giants) who descended from angels, “who fell from the heavens.”
