An important and incompletely answered question is whether a high-order rogue wave (RW) can be excited by the collision of first-order RWs, especially for its generation and propagation mechanisms. In this paper, the evolution properties of collisions between RWs are studied numerically for two-component coupled Bose-Einstein condensates. We find that whether a second-order RW can be successfully excited strongly depends on the location and time of the first-order RWs encountered. Only when the highest peaks of two RWs meet at the same position at the same time, can the standard second-order RW be triggered and its structure is in good agreement with the exact solution. Further, we demonstrate that such results are also applicable to the collision of subordinate RWs. This paper not only reveals the collision properties of RWs, but also provides a feasible scheme to generate higher-order RWs for experimental realization.