Solution:

Let each octagon side be $x.$ It is the hypotenuse of each cut isosceles right triangle, whose legs are $\dfrac{x}{\sqrt2}.$

Along one side of the square, two legs and one octagon side give $2\cdot\dfrac{x}{\sqrt2}+x=2000,$ so $x(\sqrt2+1)=2000$ and $x=\dfrac{2000}{\sqrt2+1}=2000(\sqrt2-1).$

Thus, the correct answer is B.