I have sorted out a reel of paracord to which the same happened, as part of a group.

If the string is still mostly on the core of the reel and not too mixed op at the open end you can put a stick through the center, have both ends secured in such a way that the string can only be taken off by rotating the reel.

As the end is already quite a bit of a mess you may have to guess where the center of the cord is and you will be out in one or more places and when you get to those places you will have to work hard to get the cord off.

In the case I worked on the reel had fallen apart a lot more and the only way out was un-tangling it bit by bit and cutting it in smaller lengths, 50 meter/yard kind of balls.

Even in the tangle it is in or the bigger mess it can become the cord is still in layers which go from end of spool to end of spool, forward and backward. The easiest way to take the cord off is by rotating the spool and taking the cord off away from the spool, just as you see done in shops where they sell cord and rope of spools.   
The important part now is not to let the cord get into more tangles and real knots.