A lot of republicans don't believe in evolution but they sure as hell support Social-Darwinism.

Social Darwinism was extinguished as a viable social/political/economic theory via the Great Depression. No one believes that anymore, not even the most hardcore GOPers.

Irony: Use of words for other than their literal intent.

Coincidence: The occurrence of events that happen at the same time by accident but seem to have some connection.

Then why are they cutting back on funding for a lot of social services and leaving a lot of poor people to fend for themselves?

Beaten to it.

A couple of reasons, and FTR I'm a Liberal, I'm necessarily advocating anything, I'm just trying to explain their mindset....

You have the idealistic NeoCons (and it is important to stress that NeoCons do not automatically equal Republicans or Tories) who honestly believe that government handouts do more harm then good to the poor and believe that by cutting these programs and services they're giving these people a chance to rise above the poverty line on their own merits, sort of a "pull themselves up by the bootstraps" kind of thinking.
There are many people who share this view who aren't NeoCons (Libertarians for example).

You have the small government C/conservatives who believe that the government simply doesn't have the right/responsibility to provide these services and programs. These are the people who echo the Jeffersonian vision of government being nothing but the governing branches, the military, and the post office, nothing else.

You have the fiscal C/conservatives who believe that these programs represent excess and irresponsible spending. These people represent the classical government mindset of balancing the books. Tax less and spend less, keep the government's debt/surplus right in the middle.

You have the C/conservatives who simply think the money would be best spent elsewhere, like the military or grants to big business.

Social Darwinism is the belief that the rich/ruling class are as privileged as they are because they were born "superior" in comparison with the rest of the population, and thus were enabled to clime the ranks of society due to their superiority. The belief also states that the poor are poor because they're naturally designed to be poor, and thus any government aide to them would upset the natural order of things. No one believes this anymore. No C/conservative politician votes to cut this or that program then says "to help the poor would be to upset the natural order of things."

There are much more rounded out political theories that C/conservatives base their ideology on. Social Darwinism died in 1929.
If you want to gain an understanding of modern conservative thought, read Edmund Burke.

Also some personal advice. I've had face-to-face political chats/debates with C/conservatives concerning social welfare programs and services. National healthcare, national childcare, etc....
Contrary to what a lot of hard-core L/liberals would have you believe, THEY'RE PEOPLE TOO!
In the end they want what you want, what's best for the country. We have different ways of going about it then them, but hey, that's what happens when you have a representative democracy. They aren't faceless monsters who hunch over their desks all day counting money and trying to come up with new ways to screw over poor people. They're people just like you and I who base their opinions on well-rounded ideological principals. Principals I may disagree with, but which I can respect non the less.
So it would be wise of you to take that into account and realize the right side of the aisle is comprised of real people who want what is best for themselves and their countrymen just like the left is.
Painting them as immoral goblin-people just deepens the political divide our society seems to have found itself in.

Cuz they're selfish xenophobic materialistic control freaks?

(just a theory)