Two important points in this verse:
First: "...He takes away..." can and probably should be translated, "He lifts up..." The meaning is that some branches of fruit or vegetable bearing plants can hang down into the dirt. A good gardener does just "lop them off" but "lifts them up" out of the dirt. The symbolism is a Christian "hanging down" in some sin. God will seek to lift that one out of the "dirt" so they can be fruitful.
Second: "He prunes..." meaning that God strips away unwanted activities in a Christian's life so they can concentrate on yielding fruit for the Lord. Branches are trimmed so the life-giving sap can flow into the parts of the branch that will produce fruit for God's glory.
Thank the Lord for His "lifting up" and "pruning" in your life. More fruit means glory to God and joy to your soul!