We report the first experimental demonstration of a wavelength tunable passively Q-switched red-diode-end pumped Alexandrite laser using a semiconductor saturable absorber mirror (SESAM). We present the results of the study of passive SESAM Q-switching and wavelength-tuning in continuous diode-pumped Alexandrite lasers in both linear cavity and X-cavity configurations. In the linear cavity configuration, pulsed operation up to 27 kHz repetition rate in fundamental mode was achieved and maximum average power was 41 mW. The shortest pulse generated was 550 ns (FWHM) and the Q-switched wavelength tuning band spanned was between 740 nm and 755 nm. In the X-cavity configuration, a higher average power up to 73 mW, and obtained with higher pulse energy at 11.2 kHz repetition rate, in fundamental mode with excellent spatial quality . The Q-switched wavelength tuning band spanned was between 775 nm and 781 nm.