Is there a way to take a string theory, and produce from it a string theory which does not contain gravity?
I.e., effectively remove the graviton and it's states from the theory.
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To my knowledge you have always a graviton in the closed string string spectrum.
The remaining option is to do a theory of only open strings. The problem now is that every loop interactions involves closed strings, so an open string theory is not consistent at the quantum level. See for instance the nice picture of p. 54, in Superstring Theory (Green, Schwarz, Witten)
Or, are you thinking something like a generalized GSO projection?