This is a QR model, not thru-axle? What new hub did you put on the bike?

Something's wrong here - the spacing to the disc rotor is a standard distance that has nothing to do with hub width.

Did you buy this bike new? Is the old wheel correctly dished?

Is the new wheel hitting the frame on the left or right side? Was the DT hub purchased new?

Is the old wheel really 130mm?

Redishing moves the rim in relation to the hub, and will move the rim in relation to the frame. But redishing will do nothing to move the rotor. It is in a fixed position on the hub. The fact that is it hitting the frame seems like it is either the wrong size hub or the wrong endcaps, or something with the dropouts. A picture of this would probably help. 

From everything I've read on that SCS hub, there were only a couple manufacturers who made them.  Specialized/Roval being one, and I think Hope was the other one.   I really hope you're not up a creek on this one, but I really doubt that 240 hub is ever gonna fit in an SCS spaced frame.  I am confident that DT Swiss doesn't make a disc brake hub with 130mm spacing, only 135/142mm. 

From everything I've read on that SCS hub, there were only a couple manufacturers who made them.  Specialized/Roval being one, and I think Hope was the other one.   I really hope you're not up a creek on this one, but I really doubt that 240 hub is ever gonna fit in an SCS spaced frame.  I am confident that DT Swiss doesn't make a disc brake hub with 130mm spacing, only 135/142mm. 

Redishing moves the rim in relation to the hub, and will move the rim in relation to the frame. But redishing will do nothing to move the rotor. It is in a fixed position on the hub. The fact that is it hitting the frame seems like it is either the wrong size hub or the wrong endcaps, or something with the dropouts. A picture of this would probably help. 

The SCS rear QR hub is supposed to be 135 spaced, with the drive-side flange and cassette moved 2.5mm inwards to match the chainline of a 130mm road hub:

 
You can see the disc mount remains in the same place. The special SCS hanger just moves the rear derailleur in 2.5mm to track the cassette but doesn't change the hub spacing.

The spacing from the disc mount to the end cap should be constant across all hub widths - that's why the disc mount floats out about an inch on wide tandem hubs:

 

So if your hub is making the disc hit the brake mount, there's two possibilities:

1) the end cap of the hub is wrong, but this should change the overall hub spacing.
2) the disc mount is too far inwards/crooked. This could happen on a welded bike, but this model is carbon and you would expect it to come out of the mold correctly aligned (unless the mount is bonded later)

If your correctly dished rear wheel is hitting the NDS chainstay, there's only one possibility: something's wrong with the frame.

If your rotor and rear wheel hit the NDS side of the frame, there's only one possibility: wrong end cap/missing space after the wheel was dished. But the wheel would be out of dish and your hub would be narrower.

Then the mystery of the 130 hub when it should be 135...

This is all too weird to diagnose over the internet, so let's move on: sure, you can throw a spacer on the left side and redish the wheel and as long as you can make everything fits, the bike should be fine. The only question is if you can put enough spacers in there and still get the hub to fit. 

Also if you need 1mm of clearance at the rotor you can add a 1mm spacer, but to get 1mm extra at the tire you'll need 2mm of spacers.

Though here's another question: is there a recess on the inside of the left dropout that the axle fits into?

The SCS rear QR hub is supposed to be 135 spaced, with the drive-side flange and cassette moved 2.5mm inwards to match the chainline of a 130mm road hub:

 
You can see the disc mount remains in the same place. The special SCS hanger just moves the rear derailleur in 2.5mm to track the cassette but doesn't change the hub spacing.

The spacing from the disc mount to the end cap should be constant across all hub widths - that's why the disc mount floats out about an inch on wide tandem hubs:

 

So if your hub is making the disc hit the brake mount, there's two possibilities:

1) the end cap of the hub is wrong, but this should change the overall hub spacing.
2) the disc mount is too far inwards/crooked. This could happen on a welded bike, but this model is carbon and you would expect it to come out of the mold correctly aligned (unless the mount is bonded later)

If your correctly dished rear wheel is hitting the NDS chainstay, there's only one possibility: something's wrong with the frame.

If your rotor and rear wheel hit the NDS side of the frame, there's only one possibility: wrong end cap/missing space after the wheel was dished. But the wheel would be out of dish and your hub would be narrower.

Then the mystery of the 130 hub when it should be 135...

This is all too weird to diagnose over the internet, so let's move on: sure, you can throw a spacer on the left side and redish the wheel and as long as you can make everything fits, the bike should be fine. The only question is if you can put enough spacers in there and still get the hub to fit. 

Also if you need 1mm of clearance at the rotor you can add a 1mm spacer, but to get 1mm extra at the tire you'll need 2mm of spacers.

Though here's another question: is there a recess on the inside of the left dropout that the axle fits into?

I'm not sure if I can add anything new to this.  And will likely only add to the confusion.

...

The diagram posted above, Compatibility Guide, is, in my opinion, is consistent w/this ambiguity.  The lines shown on the SCS hub should in reality be spaced at 130mm rather than 135mm. 

That's a very good synopsis of the thru-axle situation, but the OP has a QR bike. The diagram above is for the QR hubs which you can confirm by the derailleur hanger.

But that even well-written explanations make the whole situation more confusing shows just how bad Specialized screwed up with this "standard".

So the nds flange moved in and took with it the rotor on the scs hub, while on my new wheel that flange is at a standard position.

Sort of - on the thru-axle hub the rotor is 2.5mm further inboard from the end of the axle to set it to 130mm disc spacing, but the end of the axle is recessed 2.5mm into the frame. So the rotor should be in the same place relative to the dropout.

So then the question is - does your QR frame also have a 2.5mm recess the hub fits into on the inside of the dropout even though it's not through axle? Let's assume Specialized used the same 135 hub shell and spacing on the QR and TA hubs (which means the above diagram is wrong). Because then in that case a new 135 hub would have the disc 2.5mm too far to the left. Which seems to explain the disc interference. But it doesn't explain why the wheel is also hitting the frame. But if there is a recess on the left side maybe the new endcaps don't fit the same which is making the wheel sit crooked?

What's the distance from the outside face of the rotor to the end cap?