is a mutual fund taxable

Unless the fund is in a retirement account you have to report that income. 

Sometimes.  You will get a tax statement from the fund manager, that combines a 1099-INT, 1099-DIV and 1099-B.  If the fund buys and sells shares of different stocks, that can create capital gains or losses that are reported on a 1099-B.  Dividends are reported on a 1099-DIV.  Sometimes the dividends are reinvested and not immediately taxable, sometimes they are taxable to you when paid.  Any money funds that pay interest will be reported on a 1099-INT and that is also taxable to you, even if the interest and dividends are re-invested to buy more shares.

However, you won't pay taxes twice.  If you pay taxes on the interest and dividends that are used to buy more shares, you have a basis in those shares, so you will only pay tax later on any gain in share price.