Can it be said that there was a phenomenon very similar to genocide in the Americas, wherein the Europeans intended to remove/eliminate the native populations of America in order to colonize the continent, and then ended up wiping out an overwhelming portion of them?

Yes. You may check out this FAQ page that highlights how what the European Nations and Americans did counts as genocide in every sense of the word. However, note that genocide does not just include mass killings of people. Genocide can and has occurred without a single person being killed.

Here is a copy+paste of an past answer I've given for this question.

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In the most gentle and sincere way, I want to pose this question to you. If 9,000 people die out of a group of 10,000 because of disease, then a second group of people come in and murder the remaining 1,000 because they were considered inferior and possessed land the second group wanted, is this second group free of guilt because most were dead already?

Can you provide examples where the intent was to end a group of people?

I certainly can.

Stated Intent of U.S. Officials (Criteria A)

"That a war of extermination will continue to be waged between the races until the Indian race becomes extinct must be expected."

--California Governor Peter Burnett, Jan. 6th, 1851

". . .these Indians will in the end be exterminated. They must soon be crushed - they will be exterminated before the onward march of the white man."

--U.S. Senator John Weller, 1852, page 17, citation 92

“The Sioux Indians of Minnesota must be exterminated or driven forever beyond the borders of the state.”

--Minnesota Governor Alexander Ramsey, Sept. 9th, 1862

Intent Manifested in Actions (Criteria C)

When tribes signed treaties and were moved to reservations, either by agreement or force relocation and expropriation, the U.S. Government was responsible for providing services for reservation through the Bureau of Indian Affairs. While it depended on the terms of the treaty, one service to be provided was rations. While many tribes were on this program, there is a long history of neglect on reservations by governing officials and policies that were structured so as to provide minimal care to Indians, policies that were not changed despite significant outcry.

In September of 1877, Northern Cheyennes camped at Fort Reno in Indian Territory were reported to have gone weeks without their rations. When they did receive rations, items were missing. Sickness from lack of food was prevalent among groups of Cheyennes. When beef was issued in place of these items, the animals were often "starved" and small in appearance and did not leave much meat for whole families and groups, sometimes amounting to 50 people. Even though these issues had been raised to the Indian Agent in charge, John Miles, the situation was dismissed and the prescribed allocation of rations, established by the Commissioner of Indian Affairs, were continued. An atmosphere of hostility began to develop over the food issue as now 150 people were sick.

On a separate occasion, the Dakota Indians murdered Indian agent Andrew Myrick because of the hostility created between him and the natives on the reservation under his watch. Due to a disastrous winter in 1861-1862, much of the food sources on the reservation were suffering. People were also starving. While withholding rations from the tribesmen, Myrick is infamously quoted as saying "'Well then, if you want it then you eat your grass." Myrick's "let them eat grass" remark was dehumanizing. It implied Indians were like horses or cattle.

Recent Actions Identifying Intent (Criteria D)

The Indian Health Service (IHS) is a federally run service for American Indians and Alaska Natives. It is, obviously, responsible for providing proper health care for native peoples as established via the treaties and trust relationship between tribes and the U.S. Government. However, on November 6, 1976, the Government Accounting Office (GAO) released the results of an investigation that concluded that between 1973 and 1976, IHS performed 3,406 sterilizations on Native American women. Per capita, this figure would be equivalent to sterilizing 452,000 non-Native American women.

According to the above article, many of these sterilizations were conducted without the consent of the women being sterilized or under coercion. Table 1 on page 403 of this article from the American Indian Quarterly shows a steep decline in birthrates among several Native American tribes.

Boarding Schools - Forced Assimilation is Genocide (Criteria E)

Many people are familiar with the systematic removal of Indian children from their parents and placement into boarding schools. These schools were either church or government run, but were most certainly sanctioned by the United States government as an attempt to assimilate Indians and erase their culture. The BIA own ups to this at the end of their FAQ page by saying "The Indian Reorganization Act of 1934 introduced the teaching of Indian history and culture in BIA schools, which contrasted with the federal policy at the time of acculturating and assimilating Indian people through the BIA boarding school system."

One guiding principle can be used to describe the goal of the entire boarding school experience:

“Kill the Indian, and save the man.”

--U.S. Capt. Richard H. Pratt, 1879, on the Education of Native Americans

U.S. Army Policy of Killing Buffalo (Criteria C, really check out the link on this one)

And last, but not least, is one of the best examples besides the boarding schools. In this answer here, I explain how it was the intention and policy of the U.S. Army to kill the buffalo of America off in an attempt to subdue, even exterminate, the Plains Indians.

On top of this, it's as if their cultures are almost non-existent.

Answering this out of the scope of this subreddit, but this is certainly not the case in numerous regards. Many are almost non-existent, but not all.