The term 'deportation' means the identification, detention, and removal of non-citizens from a nation (as opposed to the removal goods or objects, which is covered by the term 'exportation'). Every country has a procedure for deporting people, and most Western nations have established legal processes to determine who should and should not be subject to deportation. Historically, the US has had loose rules for immigration, particularly for those who enter the country for labor rather than seeking a citizenship path, but Trumpism (like nationalist movements generally) is expressly anti-immigrant, and so an increase in deportation-language is probably to be expected.
The problem with Trump's speech isn't the term 'deportation' per se, but with the explicit ideation of large-scale indiscriminate deportation. This is what begins to stir up images of people crammed into railroad cattle-cars and shipped to concentration camps for 'processing' and 'relocation'. Mass deportation of this sort — as the Nazis discovered trying to move Jews, Gypsies, and Communists, and the Ottomans discovered trying to relocate Armenians — is extremely cost-inefficient. People being relocated cannot produce anything of value, but must be housed, fed, clothed, provided medical care, guarded, and constrained until the moment they are sent from the territory, assuming the state can fond a foreign nation willing to repatriate them. The more people being deported, the greater the cost, and the greater the difficulties with repatriation. This invariably leads to cost-cutting and cost-recovery efforts, such as limitations on or rationing of food, shelter, water, and other necessities, sub-par medical care, overcrowding, or even the expropriation of any wealth the deported people might have or the implementation of forced labor to cover costs. In turn, these measure, lead to increases in disease, exposure, malnutrition, exhaustion, and violence in both detainees and overworked guards. Mass deportation efforts invariably carry a significant death toll, whether or not the deporting administration has any specific plan for inflicting death. The general fear is that if Trump implements this plan he will (wittingly or not) stumble his way into something like a genocide.
Argue the legalities of it anyway you like; if it happens it will be ugly.