Romans 14:14, 23 teaches us not to act contrary to our conscience. If you are convinced that it would be wrong for you even to attend the ceremony, then it would be wrong for you. On the other hand, you might be convinced that you can, in good conscience, attend the ceremony.
Your attendance or absence from the ceremony is not the most important matter here. More important is what you communicate to your family member about your presence or absence.
If you choose to attend, you can explain that you came because you love your family member, not because you agree with same-sex marriages.
On the other hand, if you choose not to attend, you can explain to your family member that you thought through how best to show love to him or her and also stand up for the truths of Scripture, and you settled on not attending.
The decision on what to do with the wedding invitation is entirely yours. Most important is what you communicate to your family member regarding your decision. Speak the truth in love to your family member (Ephesians 4:15), provide Christian witness and example, and keep your relative in your prayers. God bless you.