Generally, No.
You will have again or a loss each time you sell a position. You will pay taxes on the net gain each year (long-term and short-term gains are treated differently). This is regardless of whether you manage the funds or not. I assume that this is a money manager who is buying and selling stocks, etc.
However, if the money manager takes your funds and puts them in a pool, e.g. a mutual fund, then you are taxed each year based on the net gains/losses incurred by that fund in each year.
If so, is there a way to manage your own money/investments without paying taxes until you cash out or something similar?
Yes, well sort of … Build a portfolio based on index ETFs and hold without selling. You will have dividends, but no captial gains until you sell.
disclaimer : I am not a tax lawyer or a financial advisor. The advice above is based on personal experience.