We present a novel coreset construction algorithm for solving classification tasks using Support Vector Machines (SVMs) in a computationally efficient manner. A coreset is a weighted subset of the original data points that provably approximates the original set. We show that coresets of size polylogarithmic in $n$ and polynomial in $d$ exist for a set of $n$ input points with $d$ features and present an $(ε,δ)$-FPRAS for constructing coresets for scalable SVM training. Our method leverages the insight that data points are often redundant and uses an importance sampling scheme based on the sensitivity of each data point to construct coresets efficiently. We evaluate the performance of our algorithm in accelerating SVM training against real-world data sets and compare our algorithm to state-of-the-art coreset approaches. Our empirical results show that our approach outperforms a state-of-the-art coreset approach and uniform sampling in enabling computational speedups while achieving low approximation error.