I don't understand. Why would a support clearing the enemy traps waste your mana?
Well you see, good Sivirs will use their spell shield as a way of negating Caitlyn's Piltover Peacemaker. By standing within the creep line, they create an interesting dilemma for Cait; She naturally wants to push the wave to the enemy tower with her Q and auto attacks, where her range allows her to still farm but the enemy will lose CS to tower shots. Between her escape, her support's wards, and clever trap positioning, this keeps her safe and farmed while denying her opponent precious CS.
But if Sivir is standing within her creep, using Q is detrimental. The animation for it is extremely obvious, and Sivir has plenty of time to press E. This will recover her mana, allowing Sivir to use Boomerang Blade. The net result is that neither wave is pushed, but Caitly ends up with less mana than Sivir (and less health if she or the support were hit by the blade). This is an overall loss for her, and if it happens enough will create a favorable advantage for the Sivir player to push in order to win the lane.
Most Caitlyns are aware of this situation. They know that they cannot expect to freely push their wave against Sivir unless they can find a way to draw Sivir out of the creep wave. Placing Traps in the bush threatens bush control; A Sivir player wants to clear those traps. If the Support clears it they'll take free harass due to the DoT and snare. Sivir can clear it with her spellshield, but leaving the wave gives Caitlyn time to Q it. Sivir can Q the wave herself once she has cleared the trap and the wave will have only pushed a small amount. Many Sivir players consider that minor push to be manageable compared to the harass that a Support would take and would rather accept that then give Caitlyn bush control.
Which is not to say that every Sivir player will think that way. Ideally you will want to communicate with your AD carry to confirm their strategy for dealing with that situation. If you are playing someone like Janna, who can negate the harass with her E, or Blitzcrank, who might bait the enemy into a clear shot with his Q, it may be advantageous to clear the traps as the support. If you are playing someone like Sona or Zyra, you are better suited letting Sivir clear the trap and focusing on poking the Cait as soon as she starts the animation for Piltover Peacemaker. Regardless, let your Sivir decide what they want to do with them, as miscommunication can result in Caitlyn getting the advantage.