Assuming your logo has a transparent background:
- Duplicate the image layer and desaturate it (Color > Desaturate > Desaturate)
- Add a layer group
- Put the desaturated image in the group
- Insert the logo above it in the group (CAMPFIRE in the example)
- Set the logo layer to Erase mode.
Explanation: the Erase mode on the logo layer makes everything "in its shadow" in the same group transparent, so the result is a desaturated image with a logo-shaped hole in it, through which you see the original colors.
There is another solution, that creates a logo shaped color image over the desaturated image.