I second what Avril said. Even when practicing veganism, it is not possible to prevent violence 100%. Even organic produce is permitted to be grown with pesticides (insect poison), as long as the pesticides are not synthetically-derived: https://en.wikipedia.org/wiki/Organic_certification . Veganism serves to minimize violence, not to eliminate it completely.
Nevertheless, here are the verdicts on the ingredients in your iron supplement:
Iron (ferrous sulfate): This is a mineral, mined from the earth. Vegan.
Cellulose gel: The closest thing I found was "cellulose gum". The (vegan) Vegetarian Resource Group says this is vegan: http://www.vrg.org/ingredients/
Dibasic calcium phosphate: The Vegetarian Resource Group says this is vegan: http://www.vrg.org/ingredients/
Croscarmellose Sodiumis an internally cross-linked sodium carboxymethylcellulose. Carboxymethycellulose is made by reacting cellulose (plant fiber) with chloroacetic acid: https://en.wikipedia.org/wiki/Carboxymethyl_cellulose . Chloroacetic acid is produced from either acetic acid (vinegar) or from trichloroethylene (made from petroleum-derived gas). https://en.wikipedia.org/wiki/Trichloroethylene . Appears vegan.
Hydroxypropyl Methylcellulose is an alternative to animal gelatin: https://en.wikipedia.org/wiki/Hypromellose . Appears vegan.
Titanium Dioxide: Derived from mineral ores: https://en.wikipedia.org/wiki/Titanium_dioxide . Vegan.
Magnesium Stearate: The Vegetarian Resource Group states, "Although it is possible to derive magnesium stearate from animal fats, it is not standard practice today in the food industry and no examples of tallow-derived magnesium stearate in foods or pharmaceuticals are known." http://www.vrg.org/ingredients/
Polyethylene Glycol: Produced by interaction of ethylene oxide with water, ethylene glycol (same as your car's radiator fluid), or ethylene glycol oligomers. Ethylene compounds are produced from petroleum. Polyethylene glycol is a common ingredient in cosmetics and beverages, including my favorite drink, Dr. Pepper! https://en.wikipedia.org/wiki/Polyethylene_glycol . Appears vegan.
Triethyl Citrate: Derived from citric acid (produced from citrus fruits, certain molds, or synthetically made in a process starting with calcium salts): https://en.wikipedia.org/wiki/Citric_acid#Natural_occurrence_and_industrial_production . Appears vegan.
Polysorbate 80: May contain animal ingredient, but let's not stress out over a few milligrams of animal product, OK? Chances are, you drove over a couple of ants today: http://www.vrg.org/ingredients/
Sodium citrate: Made from sodium bicarbonate (baking soda), or from citric acid: https://en.wikipedia.org/wiki/Monosodium_citrate. Appears vegan.
I'd say this is 99.9% vegan, which is as good as you can get. Don't stress!
Nevertheless, here are the verdicts on the ingredients in your iron supplement:
Iron (ferrous sulfate): This is a mineral, mined from the earth. Vegan.
Cellulose gel: The closest thing I found was "cellulose gum". The (vegan) Vegetarian Resource Group says this is vegan: http://www.vrg.org/ingredients/
Dibasic calcium phosphate: The Vegetarian Resource Group says this is vegan: http://www.vrg.org/ingredients/
Croscarmellose Sodiumis an internally cross-linked sodium carboxymethylcellulose. Carboxymethycellulose is made by reacting cellulose (plant fiber) with chloroacetic acid: https://en.wikipedia.org/wiki/Carboxymethyl_cellulose . Chloroacetic acid is produced from either acetic acid (vinegar) or from trichloroethylene (made from petroleum-derived gas). https://en.wikipedia.org/wiki/Trichloroethylene . Appears vegan.
Hydroxypropyl Methylcellulose is an alternative to animal gelatin: https://en.wikipedia.org/wiki/Hypromellose . Appears vegan.
Titanium Dioxide: Derived from mineral ores: https://en.wikipedia.org/wiki/Titanium_dioxide . Vegan.
Magnesium Stearate: The Vegetarian Resource Group states, "Although it is possible to derive magnesium stearate from animal fats, it is not standard practice today in the food industry and no examples of tallow-derived magnesium stearate in foods or pharmaceuticals are known." http://www.vrg.org/ingredients/
Polyethylene Glycol: Produced by interaction of ethylene oxide with water, ethylene glycol (same as your car's radiator fluid), or ethylene glycol oligomers. Ethylene compounds are produced from petroleum. Polyethylene glycol is a common ingredient in cosmetics and beverages, including my favorite drink, Dr. Pepper! https://en.wikipedia.org/wiki/Polyethylene_glycol . Appears vegan.
Triethyl Citrate: Derived from citric acid (produced from citrus fruits, certain molds, or synthetically made in a process starting with calcium salts): https://en.wikipedia.org/wiki/Citric_acid#Natural_occurrence_and_industrial_production . Appears vegan.
Polysorbate 80: May contain animal ingredient, but let's not stress out over a few milligrams of animal product, OK? Chances are, you drove over a couple of ants today: http://www.vrg.org/ingredients/
Sodium citrate: Made from sodium bicarbonate (baking soda), or from citric acid: https://en.wikipedia.org/wiki/Monosodium_citrate. Appears vegan.
I'd say this is 99.9% vegan, which is as good as you can get. Don't stress!