Paul gives his personal preference here, not the perfect will of God as such. He is simply saying that, as far as his own personal, human will is concerned, he would that the people who are troubling the Galatians were cut off (amputated) from them so that they could serve the Lord in truth without any mixture of error or any temptation to yield to those who are always pulling believers away from the truth into the old Judaism.
He mentions these people in Gal. 1:7 Which is not another (Gospel); but there be some that trouble you, and would pervert the gospel of Christ. Wouldn't it be nice if everyone who troubles us in our work for the Lord were simply cut off so that they could not do their dirty work? We could simply have the liberty to live and preach what we believe the Bible says, and that would seem to be a wonderful existence.
We know that God will recompense, or repay, those who are pulling the churches away from the truth, 2 Thess 1:6 Seeing it is a righteous thing with God to recompense tribulation to them that trouble you; Good enough for them, right? Well, I do not believe that God has planned or purposed that the world be separated from us just so that we can serve the Lord without any problems. We might properly consider 1 Cor. 5:10 Yet not altogether with the fornicators of this world, or with the covetous, or extortioners, or with idolaters; for then must ye needs go out of the world.
Jesus said, in part, in John 16:33, In the world ye shall have tribulation . . . It is his purpose that we have tribulation. One reason is that tribulation works patience in us (See Romans 5:3; James 1:3). If Baptists need anything at all, they need patience, as do all believers in Christ. So, it is not God's will, though it may be Paul's will, that God "cut off" those that trouble us.
Then Paul delivers a warning to these believers in this Galatian church. He mentions their liberty in Christ, of which the Bible speaks much (Rom. 8:21; 1 Cor. 8:9; 10:9; 2 Cor. 3:17; Gal. 2:4; 2 Peter 2:16). But he in this book, as well as in other books of his, warns them about this liberty. They are not to use their liberty as an occasion to the flesh, to please the flesh, or to work, worship, or think in the flesh. God's liberty in salvation does not extend that far. His liberty is liberty from the bonds of the law in order that we may be free to serve the Lord Christ (Col. 3:24).
Using this liberty for benefit of the flesh brings about strife and divisions. In these we "devour" one another and cause divisions in the Lord's churches. But the admonition is to "love one another," which is the fulfilling of the law of Christ. Those who "trouble" us will not be cut off while we are in this world. We are to do the work of Christ despite those who trouble us. They will be here as long as we are, so we must work among them, preach the truth despite them, and love one another, using our liberty in the way God prescribes.