I am so sorry that you are having to face so many challenging things at once. Know that you're not weak for struggling to know how to deal with everything that has happened.
God will not hate you if you cut. Nothing you ever do could make Him love you any less. You are His daughter, you are His son, and He values you beyond words. My favorite Bible passage that says this really clearly is Romans 8:38-39: "And I am convinced that nothing can ever separate us from God's love. Neither death nor life, neither angels nor demons, neither our fears for today nor our worries about tomorrow—not even the powers of hell can separate us from God's love. No power in the sky above or in the earth below—indeed, nothing in all creation will ever be able to separate us from the love of God that is revealed in Christ Jesus our Lord."
However, because of that same love, God does want you to be well and not to harm yourself. This is not because He is angry, but because He loves you so much that His heart hurts when He knows you are hurting. In Hebrews 4, the Bible tells us that Jesus understands what we're going through because He was once human too, dealing with all the challenges of living in this confusing, painful world. He wants us to have joyful, vibrant lives (He says this in John 10:10). He wants to help us hope even in the really hard times.
It's important to know also that you don't have to do this alone. God is with you, but He also intends for us to let other people help us too. If there is anyone in your life you can trust, whether it be a family member or a pastor or a school counselor, it's very, very important to let them know how you're feeling. They will be able to help you find healthy ways to deal with all the stress that don't involve harming yourself.
Some healthy things to do when you feel like cutting might be going for a walk, calling a friend, writing in a journal, watching a favorite movie, or listening to music you love—anything that channels all that anxiety and pain you're carrying into an action that is healthy. The things we keep bottled up inside have to escape somehow. It will help to find some ways to help the feelings escape that are beautiful instead of harmful.
Finally, know that you can outlast every one of these storms in your life, even though it doesn't always feel like it. In Romans 8, it says "the Spirit of God, who raised Jesus from the dead, lives in you." For those who believe in Jesus and follow God, the same Spirit that literally changed death into life lives inside them. If that is true of you, then that strength can make you strong too.
God loves you so, so much.
Elraen is "a rescued failure" and strives to learn to live a song of redemption. She loves music because she has seen how it can breathe, the way it makes people come alive. She takes pictures and goes to shows and writes for a major Christian music website.