On the basis of the spin-polarized density functional theory calculations, we demonstrate that partially open carbon nanotubes (CNTs) observed in recent experiments have rich electronic and magnetic properties which depend on the degree of the opening. A partially open armchair CNT is converted from a metal to a semiconductor and then to a spin-polarized semiconductor by increasing the length of the opening on the wall. Spin-polarized states become increasingly more stable than nonmagnetic states as the length of the opening is further increased. In addition, external electric fields or chemical modifications are usable to control the electronic and magnetic properties of the system. We show that half-metallicity may be achieved and the spin current may be controlled by external electric fields or by asymmetric functionalization of the edges of the opening. Our findings suggest that partially open CNTs may offer unique opportunities for the future development of nanoscale electronics and spintronics.