Embroidery adds beautiful embellishments to clothes; it can be hard to imagine a scenario where you would want it removed. Good, stable embroidery should NOT be able to be removed easily. There is a risk of making a hole or ruining the area that is embroidered. Also, keep in mind the area with the original embroidery is “compromised” — already has the tiny needle holes so the new stitching will be difficult to adhere to the fabric. Removing embroidery takes a lot of time and patience, and there is a cost associated with this. It is NEVER recommended.
For smaller bits of embroidery, using a seam ripper can work. Turn your embroidery over and work from the back, carefully cutting the stitches with the seam ripper. Lift the seam ripper upwards at an angle to rip the threads, working a few stitches at a time. Beware of ripping the fabric of the garment. Return to the front of the embroidery and pull the stitches out; you can use a darning needle to lift the thread away, or a pair of tweezers. If there is any resistance, turn the embroidery back over as you may not have cut a stitch all the way through.
98% of the time, removing embroidery is not worth the time and expense. Fabric can become damaged or could become deformed during the process. For example, stretch fabric is not recommended for embroidery removal, as there will be visible holes / outlines from the original embroidery.