Note that there are three mitzvos according to the Rambam that have to do with Amalek.
- Destroy the remnant of Amalek (Positive #189)
- Remember what Amalek did (Positive #188)
- Don't forget what he did (Negative #59)
The Ramban agrees. The Semag also counts these three (Asin 115, 116, Lavin 226).
Rav Yerucham Fishel Perlow points out that Rav Saadiah Gaon only explicitly counted #1. You're asking why there's a need for both #2 and #3, but Rav Saadiah Gaon left both of those out. He also points out that the Bahag also only counted #1. He explains that the Bahag and the others who followed him understood that remembering what Amalek did and not forgetting are all included in the mitzvah to eradicate the remnant of Amalek. He writes:
דענין הזכירה הוא לזכור החובה למחות זרעו וכל אשר לו. וכן הוא בפסיקתא רבתי (פי"ב) הוו זכורים לו למחות את שמו מן העולם. זכור את אשר עשה לך עמלק תמחה את זכר עמלק עיי"ש.
The point of remembering is to remember the obligation to wipe out his descendants and all that is his. This is also in Pesikta Rabbasi (Chapter 12): "Remember him to wipe out his name from the world. Remember what Amalek did to you; wipe out the memory of Amalek".
It's one thing to include remembering in the mitzvah or eradicating, but why leave out the negative mitzvah against forgetting? To answer this, Rav Perlow brings the opinion of Ibn Ezra (Yesod Morah Sha'ar Sheni), who asks like you, that there's no reason to count both remembering and not forgetting. The not forgetting is just a way to strengthen the obligation to remember. He writes similarly in his commentary to that verse.
Rav Perlow explains that it must be that the Rambam, Ramban, etc. disagree. He brings the Ramban's opinion (Kiddushin 34a) that the positive mitzvah of building a fence on one's roof is the primary mitzvah, and the negative mitzvah of avoiding spilled blood on your property is secondary. Nevertheless, it's explicit in Sifrei Devarim (229) that they're two mitzvos, even though the negative mitzvah merely strengthens the positive one.
So it seems to be a dispute when the negative mitzvah is merely to strengthen the positive mitzvah, if they're both to be counted. You understand like the Ibn Ezra, whereas the Rambam et. al. see it differently. We see many other examples of this, one of which is the building of a fence on one's roof, as mentioned above.
As an aside, Rav Perlow, for unrelated reasons, wants to suggest that Rav Saadiah Gaon also counts a separate mitzvah to remember what Amalek did, and includes it in the mitzvah to read the megillah on Purim. Again, for unrelated reasons, Rav Saadiah Gaon doesn't count the negative mitzvah against forgetting (Rav Saadiah Gaon almost always only counts one mitzvah when there is a positive and negative version, and picks the one that's more inclusive). This would make him similar to Ibn Ezra, albeit for slightly reasons.