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Andrew Jackson certainly did try to get Indian tribes out of Georgia - the whole southeastern United States, really - and caused the First Seminole War, enacted a policy of Indian removal, and instigated the Trail of Tears.

Prior to Presidency

Prior to becoming President of the United States, he reach the rank of major general in the U.S. military. During the making of the Treaty of Fort Jackson in 1814, he resolved the war that had ensued with a group of Creek Indians known as the "Red Sticks." In doing so, he also applied all the consequences intended for the Red Sticks to the entire Creek Nation, including his own Indian allies during the war. One of these consequences was the loss of nearly 8 million acres owned by their Creek allies.

The above is one example of his sentiments displayed toward Native Americans during his time in the military.

Presidency

In his Second Annual Message to Congress, he offer rhetoric that makes it seem like he was in favor of supporting Native American tribes. A quote:

"It gives me pleasure to announce to Congress that the benevolent policy of the Government, steadily pursued for nearly thirty years, in relation to the removal of the Indians beyond the white settlements is approaching to a happy consummation. Two important tribes have accepted the provision made for their removal at the last session of Congress, and it is believed that their example will induce the remaining tribes also to seek the same obvious advantages."

Despite his good words, he proved contrary to them. While I don't support using Wikipedia as a source, this background information sums up nicely how Andrew Jackson felt about Indians during his time.

Because of high demand for Indian lands and the hostility between both Indians and white settlers, Andrew Jackson signed the Indian Removal Act, as cited above. While the relinquishing of lands was "voluntary," according to the act, this did not stop U.S. soldiers from entering Native lands in 1838 and forcibly removing Indians who did not want to give up their land.

Andrew Jackson notoriously fought against Federal Indian Policy as well. In 1832, the Cherokee won a Supreme Court decision protecting some of their rights as a sovereign nation. Jackson is said to have scoffed at the court's decision, declaring of the chief justice, “John Marshall has made his decision. Now let him enforce it!”

Conclusion

It is well documented that Andrew Jackson had no love for Indians. He waged war against them and personally fought them. His hand in creating the Indian Removal Act makes him culpable in the Native American deaths that occurred as a result of their removal and forced relocation. The reason they wanted to move them west of the Mississippi is because not many Americans at the time believed they would push far beyond the river. Out of sight, out of mind kinda thing, y'know?

Edit: Also, a good source on the history of the Federal Indian Policy is Indian Tribes as Sovereign Governments (Second Edition) by Charles Wilkinson & The American Indian Resources Institute.