In this paper we report cross-section measurements for $Xi^-p$ elastic and inelastic scatterings at low energy using a scintillating fiber active target. Upper limit on the total cross-section for the elastic scattering was found to be 24 mb at 90% confidence level, and the total cross section for the $Xi^-ptoLambdaLambda$ reaction was found to be $4.3^{+6.3}_{-2.7}$ mb. We compare the results with currently competing theoretical estimates.