Different from conventional materials, structures with a negative Poisson's ratio (NPR) contract/expand laterally under a longitudinal compressive/tensile strain, usually exhibiting peculiar features. Through first-principles calculations, we investigate the electronic and transport properties of Pd9B16 molecules. Its Poisson's ratio is found to be negative under uniaxial strain along a specific direction. By contacting with Au nanowires, atomic Au chains and atomic C chain electrodes, two kinds of transitions for transmission states could be realized by the modulation of the strain and the contacting site, i.e., metallic-semiconducting transition and spin polarized-unpolarized transition. Further analysis shows that it is the suppression and shifting of density of states, caused by the strain or contacting electrodes, that trigger the transitions. Those findings combine NPR and spintronics at the single-molecule level, which may throw light on the development of nanoelectronic devices.