To sing with the type intensity you hear from singers such as Dave Grohl without blowing out your vocal chords or making your throat raw requires both proper technique and some stamina (as well as certain precautions).
First let's talk about stamina. Singing involves many muscles in the face, mouth and throat but the most important muscles used in singing is the diaphragm which can be controlled by the the internal intercostal muscles and abdominal muscles that work in conjunction with the diaphragm (the diaphragm itself is an involuntary muscle). These muscles are able to push a large volume of air from the lungs and using the diaphragm as the primary means of pushing the air across your vocal chords will reduce the strain on your throat.
The diaphragm muscles and the abdominal muscles that work in conjunction with contraction of the diaphragm, can be strengthened with exercises that won't damage your throat or vocal chords. One excellent way to strengthen these muscles is to put a weight (such as a barbell weight plate) on your stomach while lying on your back and push it up and down as if you are doing it with your stomach. In other words force your belly to rise and fall as much as possible with each repetition. Do this exercise two to three times a week. It's essentially weight lifting for the muscles (the ones you can actually strengthen)used in singing.
A stronger diaphragm and supporting muscles, means less effort will be required to push air across your vocal chords.
As far as technique, you should avoid singing with your throat. Many singers tighten their throat muscles to sing higher notes. If you do this, you will become hoarse and get a scratchy throat and your vocal cords will become inflamed. If you are tightening your throat too much, your vocal chords will be straining to push sound through a constricted airway in your tightened throat. To some extent tightening of your throat will tighten the muscles surrounding your vocal chords and force them to work harder to vibrate.
Try this exercise. Sing a note that is in the higher end of your range. If you are like many folks, you may feel a tightening of the throat as you sing the higher notes. Next try singing that note while making a conscious effort to push air from your diaphragm and keep your throat relaxed. It takes practice to learn to sing without constricting your throat but if you plan to sing like Dave Grohl very often, it will be necessary to learn to do this.
I should mention that not everyone has the vocal range to comfortably sing like Dave Grohl. You should never be straining to sing outside of your comfort zone.
Other things that you can do to minimize strain on your voice is to warm up before singing and/or begin your performance with some easy to sing songs that don't require belting or high intensity and are in the lower part of your range.
Another thing that is important is to stay hydrated. This means drinking plenty of water before (starting the day before) your performance, during your performance and after. Avoid caffeine and medicines or other substances that have a diuretic effect.
Separate from hydration is lubrication of the throat. Water will help you stay hydrated but it's not actually a "lubricant" (although if your throat is dry it will definitely help). For lubricating the voice I use raw honey and coconut oil. These natural food sourced lubricants will actually coat your throat and protect it. Some folks I know use cough drops. Just don't sing with a cough drop in your mouth or you might accidentally inhale it and someone will have to do the heimlich maneuver on you. I have tried the syrup in pineapple juice before as it seems pretty slippery, but I think the citric acid may actually cause my throat to tighten up so I quite using pineapple juice.
Although many rock singers smoke, I would recommend avoiding any type of smoking if you want to preserve your singing ability.
It is also important to take periodic breaks during your performance to allow your vocal chords to rest and recover. A fifteen minute break after every 45 minutes of singing will go a long way towards preventing overuse injury. You can even take breaks by allowing other singers to help with the lead singing duties on certain songs or playing an instrumental as part of your set.
Finally, it's a good idea to have a few rest days between performances to allow your vocal folds to recover from whatever stress you put on them while singing. If you are a rock star on tour and have back to back dates on successive nights, try not talking any more than absolutely necessary between shows.
In summary, building stamina in your diaphragm and the muscles that assist it will allow you to more effectively use proper technique to minimize damage to your vocal chords and throat.