You can achieve this using a combination of smart filters & clipping masks.
- First create all the shapes you want to use as blurred areas and add them to a new group
- With the background image you want blurred selected go to
Filters -> Convert for Smart Filter. This will convert the image to a smart object and allow you to apply filters non-destructively. (It's important to do this before duplicating the layer so that any future changes will automatically update both the background and the copy)
- Duplicate the background image and place above the group in the layers panel
- Apply your desired blur (as a filter) to the copy of the background
- Create a clipping mask from the blurred copy. Do this either by ALT+CLICK between the blurred layer and the group or by selecting the blurred layer and selecting
Layer -> Create Clipping Mask
You can then use blending modes or opacity etc if you want the color of the shapes to show through.
You can then move/change anything in that group and it will show a blurred version of the background. The fact that the background is a smart object means you can also edit the background and it will automatically update the blurred copy too.
Adding all the shapes to one group isn't essential, but you will need to duplicate the background layer and add as a clipping mask for each different shape otherwise.