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I haven't done it but I've seen it done. You'll have to cut through the full depth of the block (as you would expect), and that angle grinder would probably help even out any inconsistencies from block to block.
Unless the stairs are on a solid concrete footing, mortar isn't going to work. But there's no reason you can't use adhesive. You just have to brace all the cap work until the adhesive has a chance to set up.
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