We see in the Bible that God is not a stoic, unfeeling, unemotional God. Rather, He is a God full of powerful emotions, expressing joy (Mt. 25:21, 23, Lk. 15:7) and pleasure (Ps. 115:3, Lk. 3:22) and joyful singing (Zeph. 3:17) and sorrow (Matt. 23:37, Jn. 11:35) and regret (1 Sam. 15:11) and grief (Gen. 6:6, Eph. 4:30) and anger (Ex. 32:10) and many other emotions.
We can now make sense of these passages in the Bible that describe Him as an emotional Being, because God’s relational mutability allows Him to experience these emotions. This is how we can understand God expressing anger and wrath and sorrow and regret and joy and gladness and satisfaction and pleasure. Unlike us, His emotions are pure and holy and good, never tainted by deficiencies or sin or weakness. Rather, God experiences emotions in way that is pure and totally appropriate and righteous for whatever situation He is encountering. And because His relational mutability is based on His immutability, therefore His sovereignty, foreknowledge, complete self-sufficiency, etc… are not in any way diminished.
Some people would argue that the emotions of God are anthropomorphic. Anthropomorphism is when Scripture presents God as transcending the very finite human qualities it elsewhere attributes to Him. For example, when the Bible talks about “the arm of God”, we know it is anthropomorphic because elsewhere it speaks of God being Spirit. God doesn’t really have a physical arm the way we do, but rather the writer is expressing a truth about God using finite human attributes. So are emotions also anthropomorphic? To answer that, we would have to ask, Does the Bible ever teach that God transcends emotions? And the answer is no. Therefore, we see that in the Bible that God’s emotions are a real part of who God is. In fact, I would argue that it is our emotions that are theopomorphic (to make up a word). In other words, the reason we have emotions and are emotional creatures is because God is the one that has real emotions and we are created in His image. The emotions of our hearts are merely a small flicker compared to the blazing sun that is the heart of God.