I heard that we don't have to give maaser from our income nowadays because we are outside of Israel and without the Beit Hamikdash. Is this true?
There is the Biblical commandment on tithing produce grown in the land of Israel (irrespective of the Temple's standing). Israeli farmers still tithe today; however, as the tithed produce has no special religious properties, a farmer can say "I won't give this to a Levi until/unless he proves that he's truly a Levi", and as that doesn't happen today, the farmer then eats the tithed produce too. (Except for a tenth of the tithe, i.e. 1% of the original, which has sanctity and must be left to decay. Also before tithing they take a small amount as terumah, which also must be left to decay.)
There is a separate, strongly-normative practice known as maaser kesafim ("tithing of monies") that applies on income (minus business expenses) anytime, anywhere. While there is some discussion on this, it appears the prevailing opinion is that tithing of funds (as opposed to the general obligation of charity) is a very, very good thing that absolutely should be done, but is not quite called an absolute "obligation."
I hope that helps clarify the difference between them.
There is a three way argument of the source of Maaser on money (Is it from the Torah, Rabbanan, or custom).
Either way one is fulfilling the commandment of giving tzedakah (which is obligated outside Israel).