How do I opt-out of the Social Security system and give up my Social Security Number? If I do this, am I then exempt from paying Social Security income tax?
To give up your Social Security number, you would probably have to renounce your citizenship, since merely leaving the United States, becoming a permanent expatriate, etc. wouldn't be enough.
Paying Social Security taxes is mandatory, however. Even if your income exceeds the means testing limits, you are still required to pay Social security (FICA) taxes on the income that falls beneath it.
That being said, there are several groups that are exempt from paying Social Security taxes, based on what I can scrounge up through online searching.
If you aren't part of one of these groups or you joined them after already being enrolled in the Social Security system (i.e. paid FICA taxes, etc.), you don't have to take Social Security payments, but you are not exempt from FICA payroll taxes. This means that you can't simply become Amish and be exempt if you've already paid into the system.
Many of these answers were listed here, but the only stated source is "Wikipedia," so take it with a grain of salt. I've tried to provide other sources where I could.
I mentioned that the situation with ministers and/or religious officials is more complicated. Among other things, these officials need to certify that they are religiously opposed to receiving public insurance benefits and they have to file by a certain deadline soon after earning a certain amount as a minister. Furthermore, if you file this exemption and choose/chose to revoke it later on, e.g. by filing IRS Form 2031, during the short time windows when this is possible, you're no longer eligible to file for another exemption. Once you revoke your exemption, you won't get another one.
Also note that this opt-out only applies to income earned as part of your ministry. For non-ministerial income, you're still required to pay FICA taxes even if you follow the procedure(s) above.
If you do opt-out
Clearly, opting out of the Social Security isn't easy, or even feasible, for many people, but if you are outside the system, common sense dictates that you should insure yourself against risks that would usually be covered, at least in part, by Social Security. Dave Ramsey maintains a list of such investments that he recommends ministers and religious officials who opt out of the Social Security system should purchase, but the rationale applies to anyone who isn't part of the system.
Depending on your circumstances, it's may be a good idea to invest in some or all of these instruments anyway (especially tax-advantaged/tax-sheltered retirement accounts), because Social Security doesn't cover 100% of the risks you'll face, but that decision is highly specific to each person/family.
Once you have a number you are in the Social Security system. There is currently no method that will allow you to remove your records from the system, surrender your rights to the contributions you have already made, surrender your rights to claim benefits should your qualify, or avoid paying social security payroll taxes on qualifying income.
There are some ways that you can become exempt and they can be found here. You should note the qualifier for the religious exemption that was suggested by @Muro:
So if you have ever paid into FICA, or if your parents ever received SS/Disability while you were a dependent then you probably do not qualify for that exemption. The Social Security Administration is notorious for rejecting initial applications for status changes seemingly with out looking at them. I have never heard of anyone under the age of 64 having their initial application accepted. They are also rather slow. Wait times of 6-8 months for initial rejections are not uncommon and then another 12+ months of the appeals process seems to be the norm.
Bottom line, Chances are you will not qualify for an exemption if you intend to stay in the US, and/or retain US Citizenship. Even if you can qualify expect a battle from the SSA before the status is recognized.
I did find one possible exemption on the IRS Site that exempts clergy. So if you are a full time clergy of a qualifying church you can review this site to see if you would qualify. This is not going to remove you from the system but so long as it is your only income you could avoid paying the tax in this manner.
Be aware that if you attempt to use any of the exemptions and are trying to game the system just to avoid paying the taxes it could count as what the IRS Deems Abusive tax avoidance which can result in both jail time and heavy penalties and fines.
I am aware of only one way to become exempt from paying social security taxes: become amish.
You can't opt out, and you can't exempt yourself from taxation. Except perhaps by permanently emigrating from the United States.