I see this occasionally and hear this more often.

Problem:
This is a misspelling or mispronunciation of a verb.

Explanation:
“Surpress” — spelled S-U-R-P-R-E-S-S — is a mispelling or mispronunciation of the verb “suppress”, which is spelled S-U-P-P-R-E-S-S.

Given that the first “p” in “suppress” is not usually pronounced, I believe that many American English speakers do not realize that “suppress” is spelled with two “p”s.

However, given the tendency by some speakers to add an “r” to “uh” sounds — as in “idea” pronounced “idear”, or as in “Usher” pronounced “Ursher” — it is not surprising to me that “suppress” can become “supress” instead.

The verb “surprise” is yet another source of interference.

For fun, I searched Google for each of the following words (without the quotation marks) and got about the indicated numbers of matches:

• “suppress” — 18,400,000 matches
• “surpress” — 121,000 matches

This tells me that Web authors have written the word correctly vs. incorrectly by a ratio of 152:1, which is very good but not excellent.

Solution:
“Suppress”