I've seen P&S cameras use up a roll in two ways:

1. The film is inserted, the back closed, and then the camera pulls the whole roll onto the take-up spool. As you shoot, each from is "advanced" back into the cassette. When you hit the end, what you've shot is already in the cassette.
2. The film is inserted, the back closed, and the camera then advances to the first frame. As you shoot, the film is advanced onto the take-up spool. When you hit the end, the whole roll is then rewound.

The manual for your camera leads me to believe that it uses method 2 above.

The problem here is that, if your camera does use method 2, then every frame you've shot is sitting on the take-up spool and was fogged/burned¹ when you cracked² the back. These frames are lost and there's no point in even attempting to get them developed. The only way you have any frames worth saving is if you got the camera to rewind some frames before you cracked² the back.

If I'm wrong and your camera uses method 1 above, then the frames you've shot are safely stored in the cassette as you shoot them and you can do as Alan says - simply cut off the exposed portion and go get what you have shot developed.

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General best practice when shooting film - carry a change bag with you (something like this). They're inexpensive, fold up small, and weigh very little. Easily carryable in your camera bag.

If this ever happens to you in the field, use the change bag to crack² the camera in total dark, yank the film, and rewind manually - so that you can save your shots.

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1: The use of the term burned in this context is slang for severely overexposed, to the point that the entire frame appears as one large dark spot. Thus, appearing "burned."

2: The use of the term cracked in this context is slang for opened the camera back.