The block in the picture look lkie knock-out block. The reliefs are cast into the center webs so they can be hammered out easily for use as a bond beam. You wont be able to cut dep enough with a grinder in the center webs, so I would recommend getting the right block from a masonry supplier. You could rent a 14" concrete saw to saw deep enough, but you're probably farther ahead just buying the right block.
Does the rebar need to be in the center of the block? Can it be right at the top edge joint where two blocks meet. Should be simple to knock a chip out of the edge of the webs with a brick hammer to let a rebar sit on top of the block.
Those are called RSBB units. They have holes in the bottom and are designed to be used with vertical and horizontal rebar. If that is all you have instead of solid bottom BB, then you can use a product like grout stop or even roofing shingles laid over the cores that you do not want to fill. The horizontal rebar is located where the knockout is, centered or doubled, as the case may be.
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