Computer simulations in conjunction with molecular weight distributions, obtained from gel permeation chromatography (GPC), are used to obtain physical insights on the mechanisms of degradation of guar galactomannan, a naturally occuring polysaccharide. Two different modes of degradation, sonication and enzymatic hydrolysis, are compared. Both modes of guar degradation reveal similar features in terms of changes in molecular weights, a rapid reduction followed by a slow decrease. However, the molecular weight distributions are significantly different, with ultrasonication leading to a narrowing of the molecular weight distribution and enzymatic hydrolysis resulting in its broadening. Sonication of guar results in a random degradation of chains, so that all bonds have equal probability of cleavage. In contrast, enzymatic degradation does not follow any of the typical modes of chain scission (random, Gaussian, and central), indicating that enzymatic hydrolysis of guar does not obey a "single scission" pathway. Plots of the zero shear viscosity, eta (o), as a function of number-average molecular weight, M-n, show enzymatically degraded guar to possess a much higher viscosity compared to a sonicated guar, at the same M-n. This contrasts the behavior of zero shear viscosity, eta (o), vs weight-average molecular weight, M-w, where both systems are identical despite the large differences in polydispersity. We infer that, for polydisperse systems, the steady shear rheological properties are not very sensitive to the entire molecular weight distribution and can be adequately described by M-w, the molecular weight average that is primarily controlled by the high molecular weight fraction.