Can I remove myself from someone’s Will?

If you are listed as a benficiary in a Will, you can "renounce" or "disclaim" your gift. In other words, you can choose not to accept your inheritcance.
For a disclaimer to be valid it must be in writing, be an irrevocable and unqualified refusal to accept the asset or any interest in it, and be delivered to the executor within a certain period of time from the date of the decedent's death (this period varies from jurisdiction to jurisdiction). Further, the person signing the disclaimer cannot direct that the gift go to another recipient; the Will determines to whom the property passes.
For further information you can contact the local probate court or a probate attorney in the area.

No, you can't remove yourself from another person's will (you do not have any say over what they put into their will), but also cannot be made to inherit anything against your wishes. You have the right to disclaim, or refuse, any inheritance in whole or in part, and whatever you disclaim will then be divided up amongst the other heirs. Or you could accept the property and donate it to charity.