Based on the vector diffraction theory, this paper investigates the focusing and propagation characteristics of a Bessel-Gaussian beam with a power-order mixing helical-conical wavefront. It discusses the focused light intensity, optical gradient force distribution, and propagation characteristics under different parameters in detail. The results show that the topological charge number L can finely adjust the opening of the spiral-like curve at the focal plane. The power order n can adjust the energy distribution in the focus area. By increasing the eccentricity parameters K, the position of the maximum intensity spot will move along with the y coordinate axis. When the beam parameter β increases, the number of intensity peaks on the focal plane increases. As the propagation distance z increases, the pattern of intensity distribution will change from an ellipse to "doughnut-like." Then a circular dark core will appear in the center of the light, and the propagation mode will gradually become an optical trap. Some optical gradient force distributions also are investigated to illuminate the applications of these alterable focal patterns.