One creature omitted from the 5th Edition MM is the Dragonne, and I have considered modifying stats for the manticore to create a 5E dragonne. Most of the changes would be cosmetic except for removing the manticore's tail spikes (which, if I'm right, a dragonne would not have). How far should the monster's challenge rating be reduced once this mode of attack is removed?
When the Monster Manual's Manticore (page 213) uses its Multiattack, it can either combine a bite and two claw attacks, or it can make three tail spike attacks. A bite and two claws comes out to 19 damage, on average, and three tail spikes deal a combined 21 damage, on average. The DMG tells us to make CR judgments based on the more damaging option available to a monster, so the Manticore gets to use 21, but our spikeless Dragonne is limited to 19.
Looking at the Monster Statistics by Challenge Rating table (DMG 274), 21 damage per round is in the range of a CR 3 monster. 19 damage per round is in the range of a CR 2 monster. The cutoff is 20/21, so this is a fairly fine distinction we're making.
However, as described under "Final Challenge Rating" (on the same page), monster CR depends on other factors. The Manticore's HP falls in the CR 1/2 range, and its AC is in the CR 4 range, so its Defensive Challenge Rating comes in at 2. Our Dragonne's new damage per round is in CR 2 range, and its attack bonus is in the CR 4 range, so its Offensive challenge Rating is 3.
We get the final average rating by calculating the average of the monster's offensive and defensive challenge ratings: 2.5. "Round the average up or down to the nearest challenge rating," the DMG says. According to the text, we're free to treat the Dragonne as a CR 2 or a CR 3 monster.
But all this math only confirms what was pretty obvious in the first paragraph: Numbers-wise, we haven't changed the Manticore very much. We've decreased its average damage per round by 2, which in many cases wouldn't be enough to affect the CR at all.
Removing the Manticore's tail spikes may be an important change strategically: The Manticore is (roughly) as dangerous at range as it is in melee, but our Dragonne doesn't have a ranged attack. The DMG's guidelines for monster creation and CR calculation don't say anything about the difference between ranged and melee attacks, though, which means they don't affect Challenge Rating, the abstract, mathematically-defined concept, at all. Whether the Dragonne's reliance on melee has a calculable effect on how challenging it is in "real life" will come down to how you use it.