There is the same amount of risk in mutual funds that there is with investing in individual stocks. A mutual fund is just a portfolio of stocks, so if the stock market as a whole goes down, chances are so will the mutual fund.
It also depends on who is managing the fund. You should always check the past performance of the portfolio manager and compare it with other funds before investing your money.
Mutual funds also carry fees, sometimes heavy, sometimes not so much. If a mutual fund seems to be doing great, check to make sure that its fees won't dampen your returns by too much. What may be a positive return could become a negative return once you subtract the fees.
The best way to eliminate risk is just to educate yourself as much as possible, and do your due diligence.