A new scheme of ion acceleration by crossing two ultraintense laser pulses in a near-critical relativistically transparent plasma is proposed. One laser, acting as a trigger, preaccelerates background ions in its radial direction via the laser-driven shock. Another crossed laser drives a comoving snowplow field which traps some of the preaccelerated ions and then efficiently accelerates them to high energies up to a few giga-electron-volts. The final output ion beam is collimated and quasimonoenergetic due to a momentum-selection mechanism. Particle-in-cell simulations and theoretical analysis show that the scheme is feasible and robust.