Yes...lots of commercial processors buy frozen raw material used for further processing, and "refreeze" their final results. When the raw rmaterials are wholesome when first frozen, and properly frozen/maintained, further processing such as grinding and seasoning can be refrozen if needed.
The risk you run is with freezer burn, and with some meats, such as ham with high moisture content, freezing, thawing, refreezing cycles will break down the muscle fiber affecting the texture of the product which you might find unappealing.
If your thawing whole muscle or high quality trim then grinding, you are already altering the texture, so no worries their. If you are uncertain of the wholesomeness of your frozen trim, thaw it, cook a little and taste it. If it tastes ok, then you can expect it to perform ok in your recipe.