How does your tradition handle wrathful, savage, or destructive deities?
This is a question that I come at from two different approaches because of the fact that I practice a blended faith. Generally, I give the more savage and destructive deities fairly wide berth in my practices. It is a case of if I don't attract their attention, I find my life tends to go more smoothly. There are times, however, that the deities that I do work with will fall on the destructive, wrathful, or savage side of the ledger. (One of my patron deities is Loki, the Norse god of Chaos. He has his destructive times, don't let anyone tell you otherwise. If they are, they're trying to sell you something.)
When I encounter wrathful deities, my first approach is to question if anything I have done has caused their anger. I strive to clarify the reason for their wrath and do my best to learn what I might be able to do to rectify the problem. Deities don't walk around pissed off for no reason. Some of them may be more cranky then others but genuine anger/wrath usually happens for a reason. I work to learn what that reason is and then attempt to find a solution. I basically approach it the same way as I would if I encountered a person who was angry.
Savage deities are a particularly thorny challenge. (Yes, I just made a rune pun right there. I'll wait while you throw produce in various stages of decay.) I work to stay on their 'good' side. I'll give them offerings when it is asked for/demanded, if it is in my capacity to do so. When I am unable to give them offerings, I strive to negotiate some alternative that is fitting. It is however a hard thing to negotiate with a deity that may view you like a hungry person views a juicy steak. I find it is best to approach the situation as you would in handling a wild animal that has taken an interest in you.
Don't make any sudden movements, because they might pounce. Don't show fear, because they might pounce. And for the love of everything holy, make a point of doing what you can to be as inoffensive as possible. In some cases, that may mean running up the proverbial white flag and taking a submissive stance. In others, it may mean being prepared to do what you can to defend yourself. Mind you defending yourself from a deity is hard as fuck and you won't be successful 95% of the time. However, if they see that you are willing to take on that challenge, they might back off and give you enough room to maneuver yourself into a more favorable position. Because you have turned into the mouse that roared, which makes you briefly become something other then prey.
Destructive deities, I find, are different from wrathful and savage ones. Well, they might have more in common with the savages ones then the wrathful ones. I treat it like I would in dealing with a natural disaster. I have a proverbial bug out plan in place to ride out the worst of what I can imagine being thrown at me. I make preparations for the possibility that said deity might turn wrathful and I may need to make reparations. I do what I can to prepare for the potential that said deity will take an interest in me and be around for an extended period of time. Most of all, I do my best not to take the destructive business personally. Because, like a forest fire, the destructive deities don't generally care if I'm in their path when they're going somewhere. So, I do what I can to stay out of their way.
When they do take an interest in me, I attempt to divine why that is and what they're trying to teach me. Sometimes it is a case of remembering to stay down after getting my butt kicked. In other cases, there is something that needs removed out of my life/sphere of influence and no matter how much I may kick and scream, I can't prevent it. I try to accept that destruction is the flip side of creation. Some days it is easier to keep that in mind then others.
There are times where I will give offerings in the hopes that the destructive, savage, or wrathful deities will leave me and mine alone. It's been a hit or miss situation on that one. Sometimes they'll take the offering as intended and let us be. Others, they completely ignore it and do whatever they had planned to begin with. And then there are the times where it has the unintended consequence of attracting their attention. When I manage that last one, I basically apologize for wasting their time and hunker down to bear what ever they're going to do. Fortunately, the apology for wasting their time has gone over fairly smoothly thus far. Of course, my mentioning it now might have just jinxed that lucky streak.