The invention provides a sliding skip-printing mechanism for a core rod of a two-piece can printing machine. The sliding skip-printing mechanism for the core rod of the two-piece can printing machine is characterized in that the sliding skip-printing mechanism comprises a skip-printing sliding block, a skip-printing guide rail, a spring, a limiting cushion block and a cushion block driving mechanism. The skip-printing sliding block is slidably connected to a core rod support through the skip-printing guide rail, and a mandrel is arranged on the skip-printing sliding block. The spring acts on the skip-printing sliding block to force the skip-printing sliding block to move towards the rotation center side of a core rod wheel disc. The limiting cushion block is arranged on the rotation center side, towards the core rod wheel disc, of the skip-printing sliding block in a cushioning mode. The limiting cushion block is provided with a first limiting surface matched with the skip-printing sliding block. The core rod support or the limiting cushion block (44) is further provided with a second limiting surface matched with the skip-printing sliding block. The limiting cushion block has an insertion work position and a pulling-out work position, and when the limiting cushion block is located in the insertion work position, the first limiting surface is opposite to the skip-printing sliding block; and when the limiting cushion block is located in the pulling-out work position, the second limiting surface is opposite to the skip-printing sliding block. The cushion block driving mechanism acts on the limiting cushion block so that the limiting cushion block can be switched to be located in the insertion work position or the pulling-out work position.