Normally protein cleavage can be determined qualitatively on an SDS PAAG. Is there any way to quantify the same qualitative observation in terms of numbers?
Yes, there is some techniques to quantify the degraded protein product. For example, after SDS page, gel can be scanned by laser densitometry in order to quantify it. It is of course based on intensity of bands and this method is able to accurately quantify the degradation in both minute and large amounts.
If your protein has Trp residues, they will probably change their emission (intensity/maximum emission wavelength) upon protein cleavage (and unfolding of the fragments). You should have a folded structure to start with, though.