Certainly Native Americans were forcible relocated, and many did die from disease, starvation and exposure, but that was not the intent of the action.
If you prefer to call it "ethnic cleansing," be my guest. There is no question that forcible relocation of Indian tribes was the policy of the US government, and it was often carried out in ways that guaranteed large-scale deaths from the causes you mention. It's also easy to document that terror tactics were used to force compliance with this policy.
In 2000, the head of the BIA, Kevin Gover, offered a formal apology
for his agency's role in what he himself described as ethnic cleansing:
As the nation looked to the West for more land, this agency participated in the ethnic cleansing that befell the western tribes. War necessarily begets tragedy; the war for the West was no exception. Yet in these more enlightened times, it must be acknowledged that the deliberate spread of disease, the decimation of the mighty bison herds, the use of the poison alcohol to destroy mind and body, and the cowardly killing of women and children made for tragedy on a scale so ghastly that it cannot be dismissed as merely the inevitable consequence of the clash of competing ways of life. This agency and the good people in it failed in the mission to prevent the devastation. And so great nations of patriot warriors fell. We will never push aside the memory of unnecessary and violent death at places such as Sand Creek, the banks of the Wa****a* River, and Wounded Knee.
Nor did the consequences of war have to include the futile and destructive efforts to annihilate Indian cultures. After the devastation of tribal economies and the deliberate creation of tribal dependence on the services provided by this agency, this agency set out to destroy all things Indian.
While Mr. Gover said in this speech that he was speaking only on behalf of the BIA, and not the Federal Government as a whole, he made it clear that the agency was participating in an official government policy.
Many authors have noted that the distinction between ethnic cleansing and genocide is problematic. Some have argued that genocide is one of many tactics used in ethnic cleansing, while others have argued that the term "ethnic cleansing" is merely a euphemism for genocide. The latter interpretation is supported by the origin of the expression: it was invented by the Serbs as a "nice" way of describing the genocide they committed against Bosnian Muslims.
That said, "the destruction of all things Indian" was in fact the policy of the federal government.
And the language filter strikes again...