I have mutual funds. Can I write off the amount I pay a company to invest those funds?

yes and no, depending on what you mean. I can interpret your question in 2 ways:
1) you give $10,000 to a no-load mutual fund and they invest your full $10,000 but the fund company takes out their annual expenses before they distribute dividends and capital gains (profits) to you, then no, you can not write off that amount.
2) You give $10,000 to a broker/financial planner and he gives the $10,000 to a mutual fund company that charges a 5% load to invest. The fund company pays your broker/planner $500 for his work and invest only $9,500 of your money in the fund. You can't write off that $500 now, but when you sell your fund--lets say you sell for a profit and get back $15,000--to figure out your capital gains tax your take $15,000 minus $10,000 (not $9500) as your cost basis for a profit of $5,000 (not $5,500) on which you owe capital gains.

Bottom line..... no. The fees you pay are the fees you pay. The government does not give free money for you to gamble. And if you are doing a 401, Roth, Ira etc. they are already giving you a break.

Looking to write tis small amount seems small as you have to reach a certain threshold to make this writeoff worthwhile.

No, fees are not tax deductible, however if you have the mutual fund it in a registered plan, it could be tax exempt