English Translation
When you feel stressed, take a moment to breathe deeply.
As far as I can find, „durchatmen“ already implies „tief“? DWDS’s definition is literally „tief atmen“.
The “tief” makes it extra deep… 
Yes, “durchatmen” kind of implies “tief”, but it’s really more about conscious breathing to free your lungs and/or your mind - or to “catch a breath” as in “Keine Zeit zum Durchatmen!”.
It’s basically a set phrase.
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Like @pitti42 said, the “tief” is already implied, but if you explicitly add it, it adds extra emphasis.