Troubleshooting a Mazda is generally the same as troubleshooting any type of vehicle - start with a symptom checker, such as the one available at AutoZone, and enter what the car trouble looks, smells, sounds and feels like. This isolates the problem through process of elimination and you can then begin fixing the problem.
On AutoZone.com, click on the Feels Like link and click on Sluggish, which is a symptom typically felt upon acceleration. The only option on the next page is driving, and it involves the entire vehicle. The diagnosis on the following page is a clogged air filter.
Another symptom checker on Car-Trouble.com has three terms that might qualify as sluggish under Drivability. Sluggish may mean Poor Acceleration, Hesitation, or Stumbling or Loss of Power. Selecting Poor Acceleration and clicking Proceed leads to a diagnosis page that includes the air filter as one culprit, but it also lists the EGR system, fuel injection system, MAP sensor, O2 sensor, PCV valve, throttle body and vacuum leaks as possible culprits.
A site such as MazdaProblems.com can be a good place to start for investigating problems common to Mazda vehicles. The site lists recalls and is consistently updated, as of 2015.