No, it's not against grace. It's actually in full support of grace. It's to rise up out of complacency and obtain all that grace offers.
And it's most definitely not something to twist God's arm. God doesn't need arm-twisting, and it can't be done anyway. He already want the best for us, far more so than even we ourselves.
Fasting is a way to change ourselves, not God. It is a way to put down the flesh with its lower desires, and to come up to God's higher pastures. We tune out the world and its static, and tune into the presence of God.
At the same time, the body goes through a purification process. The body is designed to fast occasionally. It's like a tune-up on a car, or back-washing a pool filter. As with many things, it's best to "start low, go slow", and build up. There are many ways to fast - a number of days each week, or hours per day, or extended fasts. There are juice fasts, "Daniel" fasts, etc. Extended water fasts usually have stages - weakness, nausea, headaches, peace, empowerment, etc. If you have medical issues, make sure you know what you're doing though. And in any case, it's good to read up on fasting before getting into it.
For all these reasons, you can have a real breakthrough by fasting. But it's necessary to keep the Lord first, and watch your heart motivations as you fast.