There is no evidence that removing a skin tag will cause more tags to grow. There is no expectation of causing skin tags to "seed" or spread by removing them. In reality, some people are simply more prone to developing skin tags and may have new growths periodically. Some individuals request periodic removal of tags at annual or even quarterly intervals.
Congenital nevi are moles that are present at birth. Congenital nevi occur in about one in 100 people. These moles are slightly more likely to develop into melanoma (cancer) than are moles that appear after birth. A mole or freckle should be checked if it has a diameter of more than a pencil eraser or any characteristics of the ABCDEs of melanoma (see below).
Treat with apple cider vinegar. Get a cotton ball and soak it in apple cider vinegar until it is totally saturated. Place the cotton ball on your skin tag and hold for a few minutes. You can move the ball in a circular motion on the skin to increase absorption if you like. Repeat this process three times per day until your skin tag falls off. This method is usually quite effective. Depending on your skin the vinegar may not be as effective so you can try using apple cider by itself. 
Shaving: A combination treatment that uses electrocautery and shaving to reduce the appearance of protruding moles. Mole shaving does not remove the root of the mole, so there is no excision scar, however there is a chance it will grow back over time. This procedure is most commonly used on protruding moles in areas that do not heal well with excision (nose).
Apply tea tree oil. This oil is well known for its anti-fungal properties. Get out a clean cotton ball. Dip it into clean water and then place three drops of tea tree oil onto the ball. Wash the area of the skin tag and the skin 1” around it using the cotton ball. Repeat three times a day. This is an effective way to dry up your tag as long as you are consistent with oil applications.
The internet, of course, is full of interesting suggestions, including tying the stalk of a skin tag with dental floss or thread in an attempt to strangulate it and make it fall off. This, too, is a recipe for traumatizing your skin. Don't fall for sites hocking skin tag removal products. The right way to remove a skin tag is at the dermatologist's office. If you've been Googling "how to remove skin tags at home," you might as well stop.
Some doctors said skin tags wouldn’t grow. Some told me they would keep growing. Most of them said they would increase in frequency as a person ages, and sure enough, what did I find over my eyelid the other day — a tiny little skin tag, just where the lid rubs against my brow. For cosmetic reasons, I’d consider getting that one removed, though the thought of liquid nitrogen on that thin skin makes me shudder, as do the aesthetics of a giant Band-Aid on my face for days.
Other skin conditions such as warts and moles can resemble skin tags. Since some moles may be cancerous, it’s best to have your skin tags examined by a doctor. Your dermatologist or family doctor will be able to diagnose skin tags. They’ll likely do this through a visual exam. If they have any doubt about the diagnosis, they may also perform a biopsy.