Does S&P 500 average 10% with or without dividends

It's including dividends (and assuming immediate reinvestments)

Note that that's a long-term average - there could (and were) much lower years , sometimes many of them in sequence.
Not also that just because it did so in the past, doesn't promise it does so in the future. But most people assume so.

Here is a Drip Calculator that will allow you to compare up to 25 years of return of dividend reinvested or not.

It's true that if you are buying options, you don't get dividends. However, a pending dividend affects the price of options so indirectly you may gain or lose some benefit because of the dividend.

There are two opposite ways to handle dividends when computing an index. If you choose to ignore them, you get a price index. Most well known indexes are computed as a price index and so is the S&P 500. Or you choose to assume dividends are fully reinvested which gives you a total return index which are much rarer. To my knowledge the only major index that is computed as a total return index is the German DAX.

If not, what is the average return without any dividends? i.e., no dividends at all, not just not reinvested. I am buying options, so I don't get dividends

So you simply take the performance form the standard S&P 500

Frame challenge:

I am buying options, so I don't get dividends

While this is literally true (you don't receive a periodic payment labeled "dividend"), it is practically false in its implication. The return on the underlying that is relevant to your options profit does include dividends. (Incidentally, the same idea applies to futures.) Two ways to see this:

1. Arbitrage ensures it. Options can be sold as well as bought, and don't have a borrow fee (unlike when shorting stocks). If an options portfolio were to correspond to the S&P 500 without dividends, then a trader could short that portfolio, buy the S&P 500 stocks, and collect the dividends risk-free. (Let's assume European options so there's no early-assignment risk -- see below.) Hence, we know options must be priced so this can't happen.

2. Option pricing formulas show that call prices are discounted for the dividends to be paid before expiration -- so the equivalent of the dividends will show up as a capital gain. Note that options on indexes like the S&P 500 are generally European, so there is no early-exercise complication. For American options on an ETF like SPY, it's a bit more complicated, but a deep-in-the-money call will track the rise in price as dividends accumulate within the ETF, then will lose value overnight going into the ETF's ex-dividend day. You should sell or exercise the call before that happens, then buy it back on ex-dividend day, so you effectively keep the dividend. Holding the call that night would lose you the dividend and would be throwing money away. This is an exception to point 1 above, in that a trader cannot profit by shorting the call over that night either, because they will be assigned.