Yes, in so far as he allegedly told these lines a reporter from the New York Times and was then quoted in that way in the New York Times.
An image slightly manipulated to show the date and source:
In its surrounding context:
In text form:
Senator Harry Truman, Democrat, of Missouri, suggested that the United States helps whichever side seemed to be losing.
“If we see that Germany is winning we ought to help Russia and if Russia is winning we ought to help Germany and that way let them kill as many as possible, although I don’t want to see Hitler victorious under any circumstances. Neither of them think anything of their pledged word.”
— Turner Catledge, “Our Policy Stated”, New York Times, June 24, 1941, p 1, 7 (NYT archive subscription required)
Note: this is then subsequently always quoted to show “his firmness” towards “totalitarian adversaries”. Although at the time it was perhaps not always understood as really all that cynically “serious”, but even somewhat flexible, if not meaning that the above quote is to be read rather differently. Note the word “then” giving this a different spin:
There was another disturbing consequence of the war, and this happened at the Capitol. Several Senators and Representatives took the short view which Hitler and his advisers doubtless hoped they would take. Senator Truman proposed, though not too seriously, that the United States should help Russia to crush Germany and then, if that was succeeding, turn around and help Germany to offset the advantage. This suggestion is based on the familiar and comprehensible sentiment of “a plague o’ both your houses,” and flows from the cordial wish that both of the totalitarian States will be crushed in the combat.
— Arthur Krock: “The Government Is for Any One Who Fights Hitler”, New York Times, June 24, 1941, p18 (NYT archive)
This saying was never disputed, but also not repeated anywhere else apart from this quoted source. And the one time source is usually characterized as:
Truman’s philosophy of foreign affairs was, at best, nebulous. Just after Hitler had invaded the Soviet Union, Senator Truman had casually commented to a New York Times reporter:
“If we see that Germany is winning we ought to help Russia and if Russia is winning we ought to help Germany and that way let them kill as many as possible.”
— Walter Isaacson & Evan Thomas: “The Wise Men. Six Friends and the World they made. Acheson, Bohlen, Harriman, Kennan, Lovett, McCloy”, Simon and Schuster: New York, 1986. p256.
Compare this with how David McCullough describes this as “when asked what he thought he spoke his mind” ( — David McCullough: “Truman”, Simon and Schuster: New York, 2003. p308 gBooks)