Will Taking Down an Altar Offend Santa Muerte?
The Santa Muerte is death itself, and the power of death does not come from any altar which may or may not be standing. Altars, for many devotees of Santa Muerte, are symbols of our devotion that serve as reminders that life is finite and must be appreciated daily, but Santa Muerte is made no stronger when an altar is erected, and no weaker when an altar is taken down. Her power is perpetual and never-ending, regardless of whether or not a few trinkets are put on display. For these reasons, I do not personally think it is offensive to Santa Muerte to take down an altar.
How Should I Handle the Altar Pieces?
I recommend you treat the altar pieces with respect. This means you should handle the items with care, putting and placing them gently so as not to damage them, and storing them as you would any other item you cherish, as opposed to junk that you don't care about. It should be noted that I advise treating the items with respect not because a lack of respect would offend Santa Muerte, but because you should have respect for what the items represent. Whether you are a devotee or not, symbols of death should be respected because they represent a reminder that all life is finite and will one day come to an end, which in turn reminds us to live for the moment and to appreciate all the good things which life lets us experience.
How Can I Get Rid of Altar Pieces?
Perhaps the best way to get rid of an item that can still be used is to pass it on - give it away or sell it - so it can serve someone who would actually appreciate it. If this is out of the question for one reason or another, you could also donate the item to a second hand shop, or leave it somewhere public where it could be picked up by someone else, like on the ground next to a dumpster. If you leave the item somewhere public, you should be aware of how the item might be perceived - leaving the item exposed so it did not appear like a suspicious package, and attaching a paper with the word "FREE", would both help make sure the item was not misinterpreted.
Treating Items as Trash
All things eventually come to the end of their life cycle - even inanimate objects that form an altar. While it's a nice idea to pass on the items to somebody else who could love and appreciate them, there is nothing stopping you from treating pieces as regular trash. Perhaps the piece is broken beyond repair, perhaps the piece is associated with a bad memory, or maybe it's just a piece that you no longer feel a connection to. Whatever the reason, you should not feel as though something bad will happen just because you treated an item as regular trash - you will not take anything away from Santa Muerte by placing an Earthly trinket in the trash. When all is said and done, the Santa Muerte will still have all her power, and she will still love you.