Why did the Depression lead to the forced deportation of immigrants and especially large numbers of Mexican immigrants?

Same reason Latin American people living in the United States face today.

There were few jobs. Mexicans were willing to work anywhere they could. Meanwhile the unemployment rate among Americans was staggering, and at that time there was no backup available to make sure there was enough to eat.

The poverty among Latin Americans was very high. Deportation was actually not that hard.