I have a world where I have anthropomorphic fantastical race that was created through ritual between the humans of that world and their spirit dragons (who are like gods in a sense). The ritual in the end create these dragon/human race in my world. My question is is there a way to describe it without using terms like magic and sorcery? And I guess without making up new terms also.
I'm going to assume you mean "fantastical" or something, not fanatical, although if you mean what you said it could radically change my answer.
If you want to create a fantasy race without using those terms, just don't use them. I know it isn't very helpful, but say something like "during a ritual between the spirit dragons and the humans of the world, the ____s were created." Something like that would be okay.
I'm not sure what is wrong with those words, but the real thing I'm confused about is why you don't want to make up new terms. What do you have against that? Something like "through the ritual of _____ between the spirit dragons and the powerful ______s of the humans, the race of ______ were created or something. But there's no need to use the words magic and sorcery.
And you don't even have to make up words, just use real words for new purposes. For example, in Robert Jordans' Wheel of Time, magic is called channeling the One Power. Come up with something cool that fits with the world and the races you are creating.
Or you could just say, like, "ritual" or something. Since you used that in your description, you're probably not opposed to it.
[Tip: if you're having trouble thinking of cool fantasy-like names, use a random name generator. There are plenty of them online!]