The availability of high-power and high-brightness blue diode lasers makes them attractive as low-cost pump sources for broadly tunable Alexandrite lasers. In this paper we investigate the performance of an Alexandrite laser pumped by a high-power fiber-delivered blue diode module. Output power 1.84 W is achieved, the highest power from blue diode pumped Alexandrite to date. Excellent pump absorption is demonstrated of scrambled pump polarization on both a-axis and b-axis of Alexandrite crystal. Wavelength tuning and dual wavelength operation is produced using the self-birefringent filtering of the Brewster-cut Alexandrite crystal. An analysis is made of laser efficiency and mode formation including the creation of higher-order Laguerre-Gaussian vortex modes (LG01 and LG02). Performance is compared to red diode pumping and prospects for further optimization and power-scaling are discussed.