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Why isn't this a mistake?

You can move away the knight so your queen guards the rook. On bishop takes, you can take back another minor piece through the fork. In the end, you lose a rook and a side pawn, amounting to 6 points of material. You gain two minor pieces, which are about the same, except you still keep the strong point on E4.
Yup, 10.d5! is actually White's best move. A possible follow up might be 10...Bxb2 11.Nbd2 Bxa1 12.Qxa1 Nxd5 13.exd5 Bxd5 14.Bh6(Threatening Qg7#) Ne5 15.Nxe5 dxe5 16.Qxe5(16.Bxf8?! Qg5!(Threatening ...Qg2#) 17.f3 Qe3+ 18.Kh1 Rxf8 might be actually good for Black, who has 3 pawns for the knight and hopes for a kingside attack) f6 17.Qc3 Rf7 18.Bc4 Bxc4 19.Qxc4, where the 2 minor pieces clearly overpower Black's R+2p.
Basically, after 10...Bxb2, you play 11. Nd2! Bxa1 12. Bxa1. After this, his bishop and knight are still forked, so you win one of them. You won a bishop for a rook with the first set of moves. Overall, with this exchange, you end up winning a bishop and another minor piece for a rook and two pawns. That's not too bad an exchange, actually.
Bxb2 may win an exchange Nbd2 Bxa1 Qxa1. But now, as Anti-Hero pointed out, you win back a minor piece for a couple pawns. That makes in simplistic material terms two minor pieces for a rook and three pawns. But blacks dark squares around the king are terribly weak and his bishop can not guard them anymore. Plus you have a black squared which makes blacks situation even more dire.

Generally you can often sack the exchange, if your opponent has to give up his fianchettod bishop in front of the king and your queen gets to take back immidiately occupying the open diagonal.

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