Usually you can find the geometric mean of a set of n strictly positive numbers by calculating their combined product and finding the nth root of this product. None of the numbers can be zero or mixed positive and negative numbers. But if all the numbers are negative, you can calculate the GM by treating them as positive (just remove the minus sign), find the GM as above, and then replace the minus sign on the result. The question needs to be asked is why do you need to calculate the GM, because you need a GM which is meaningful in that context.
One way to find the GM of a set of positive and negative numbers is to add a fixed bias to each number so that all become positive. Then find the GM of these and subtract the bias. However, this method gives different results depending on the size of the bias and the net effect is to produce the arithmetic mean.
When dealing with percentages for profit and loss, you need to convert the profit and loss into actual positive amounts of money and then work out the GM of these. The result can then be expressed as a percentage profit or loss of an original amount of money.
So it’s important to ask yourself why you need the GM so that you can work out whatever would be meaningful.