If I am receiving Social Security Disability benefits would my receiving Alimony affect my Social Security Benefits?

Alimony is income if its coming your way. If you are the payor of it then it is a deduction. So if it somehow puts you over the maximum base it could affect it.

How much SSDI you get is affected by work income, not unearned income.
SSI, which is also disability but comes under state-run Welfare for those with no work history, IS affected by ALL sources of income.
Taxes are another matter entirely.
So your question needs clarification.

SS is based on qualifications which do not include income - any or all income IF you are asking about Social Security or Social Security Disability.

Or are you asking about SSI?