Mark 7:19 concludes with the words, καθαρίζων πάντα τὰ βρώματα. This phrase (“cleansing all foods”) describes λέγει (v. 18)—not εἰς τὸν ἀφεδρῶνα ἐκπορεύεται (“goes into the latrine”), the immediately preceding phrase in the text. For the participle (καθαρίζων) to modify “going out” (ἐκπορεύεται), it would have to be neuter. The subject of ἐκπορεύεται is the default, built-in pronoun, “it”—the antecedent of which is πᾶν τὸ ἔξωθεν [neuter] in v. 18c. Since the participle καθαρίζων is masculine, it can only agree with the subject of λέγει (18a), the default “he”—the antecedent of which is Jesus.
In other words, the participial phrase does not describe what happens when food is eliminated into the latrine.* That does not make food clean, especially when “clean” (καθαρίζω) refers to ceremonial cleanness!
Also note that this participial phrase comes immediately before another verb of speaking (ἔλεγεν, v. 20) which introduces Jesus’ next statement. Having interrupted his record of the dialog with this parenthetical statement (Mark’s explanation of the significance of what Jesus said), Mark must resume the dialog with another verb of speaking so the reader knows that this is not his editorial comment continuing, but Jesus’ words resuming.
It is the recognition of these grammatical considerations that serves as the basis of the paraphrastic, explanatory translations of v. 19b that are found in almost all modern translations. This is even true of the most formal equivalent translations such as ASV and NASB, as well as others moving towards the center of the formal/functional spectrum: RSV, NRSV ESV, NAB, NJB, ISV, HCSB, NIV, NET and those which set comfortably on the functional end: NLT, GNB, NCB, etc. NIV, e.g., says: (In saying this, Jesus declared all foods “clean”).
*On a related note in the preceding statement:
τὸν ἀφεδρῶνα. Masc acc sg ἀφεδρών, ῶνος, ὁ, “toilet, latrine”; elsewhere in the NT only in the || Matt 15:17. Many translations employ a euphemism, presumably to avoid “potty talk”: “out of his body” (NIV, NCV), “is eliminated” (NASB, HCSB), “is expelled” (ESV, ISV). The NRSV, NET, and NLT are among those which use a formal equivalent: “goes out into the sewer” (see also NJB, NAB). The KJV is also formal, but the obsolete word used is meaningless today: “into the draught” (OED, s.v. “draught,” XIII.45–46, gives usage current in the late 16th and early 17th C. as either “cesspool, sewer” or “privy, latrine”).