The passive voice has more focus on the subject than the action. "The most common use of passive is to indicate the subject receives the action". (Wallace)
"For a passive participle, the agent indicated by the agent marker in the context is assumed to be performing the action described by the participle".(Decker)
In this example of Going, it can be misunderstood as: As you go/ you're going, shut the door. As you have gone or having gone, baptise people. Remember that Greek has the subject embedded in the verbs.
The NET Bible notes:
“Go…baptize…teach” are participles modifying the imperative verb “make disciples.” According to ExSyn 645 the first participle (πορευθέντες, poreuthentes, “Go”) fits the typical structural pattern for the attendant circumstance participle (aorist participle preceding aorist main verb, with the mood of the main verb usually imperative or indicative) and thus picks up the mood (imperative in this case) from the main verb (μαθητεύσατε, mathēteusate, “make disciples”). This means that semantically the action of “going” is commanded, just as “making disciples” is. As for the two participles that follow the main verb (βαπτίζοντες, baptizontes, “baptizing”; and διδάσκοντες, didaskontes, “teaching”), these do not fit the normal pattern for attendant circumstance participles, since they are present participles and follow the aorist main verb. However, some interpreters do see them as carrying additional imperative force in context. Others regard them as means, manner, or even result.
Participle
Ancient Greek is a uniquely participle based language. I will quote from this site NTGreek, to explain participles, which uses Dan Wallace's book definitions in short. There are few categories described on that page.
Simple Definition of the Participle:
A participle is considered a "verbal adjective". It is often a word that ends with an "-ing" in English (such as "speaking," "having," or "seeing"). It can be used as an adjective, in that it can modify a noun (or substitute as a noun), or it can be used as an adverb and further explain or define the action of a verb.
For example:
Adjectival use: "The coming One will come and will not delay." Heb 10:37
Adverbial use: "But speaking truth in love, we may grow up into Him in all things." Eph 4:15
Introduction and Importance of the Greek Participle
Greek has been called a 'participle loving language'. "There are few languages which have equaled the Greek in the abundance and variety of its use of the participle, and certainly none has surpassed it.... This wealth of significance which belonged to the Greek participle at the zenith of its development lies undiminished before the student of the New Testament, and becomes a valuable asset in interpretation when adequately comprehended." (Quote by Dana and Mantey, pg 220.)
Use of the Greek Participle
A participle is called a 'verbal adjective' because it is formed from a verb, yet often modifies other words. Oftentimes it may be hard to to translate a participle into English and still bring out the same force as it has in the Greek. First try to understand the meaning of the Greek participle is trying to convey, then worry about an appropriate English translation. The translation may have to be as an English relative clause when used adjectivally in Greek.
The Attendant Circumstance is not much different. Its action is parallel to the main verb in the relative clause; and the mood of the main verb is usually imperative or indicative; it will reflect the same mood of its verb. The aorist tense is perfective. While translating in English, it is common to supply conjunctions like "while, when, as" in translating adverbial participles for clarity. In the attendant circumstance participle, and is usually supplied to connect it with its relative clause. It is translated as a finite verb. Few examples:
Matt. 2:13, Ἐγερθεὶς παράλαβε (take!) τὸ παιδίον καὶ τὴν μητέρα αὐτοῦ καὶ φεῦγε (flee!)
Get up, and take the child and his mother and flee to Egypt.
Mark 6:17, Αὐτὸς γὰρ ὁ Ἡρῴδης ἀποστείλας ἐκράτησεν
For Herod himself sent and seized John
Mark 9:26, κράξας καὶ πολλὰ σπαράξας ἐξῆλθεν
[The demon] cried out and convulsed [the boy] severely and came out.
Acts 10:13 (Rise, Peter;) kill and eat.
Θῦσον καὶ φάγε.
Exodus 5:18 LXX
Go and work.
πορευθέντες ἐργάζεσθε
Luke 16:6 Sit down quickly and write fifty
καθίσας ταχέως γράψον πεντήκοντα.
Acts 5:5 but when Ananias heard these words, he fell down and died
ἀκούων δὲ ὁ Ἁνανίας τοὺς λόγους τούτους πεσὼν ἐξέψυξεν·
We can notice this participle construct is used to call for a quick action, as soon as possible. Therefore, it won't be wrong, if not better to supply the adverbial conjunctions of quickness in translating this. In the great commission, Jesus is sending them immediately, without any delay. Go quickly, hurry up. Herod hastily sent and seized John. The demon instantly cried out and convulsed. Ananias died instantly. Luke 16:6 has quickly already supplied with it.
The end of the 19th century started a great interest in making a more literal translation, thus we find some translators using English participles as much as possible. I found three such examples, Godbey, Worrell, and Douay-Rheims that use "Going" in the verse. Such a translation is very unnatural, even though the such literal translations are sometimes helpful for their unconventional open minded approach.
Godbey New Testament
Going, disciple all nations, baptizing them into the name of the Father and of the Son and of the Holy Ghost.
We are to understand the participle as adverbial adjunct. For example, in Matthew 8:26, "Then getting up (εγερθεις) he rebuked the winds and the sea, and there was a great calm," Jesus is described as being raised passively. In the topic's verse 28:19 As you go; after having gone, make disciples. Matt. 2:13, Ἐγερθεὶς getting up, take the child.
See 'Grammar of obedience' chapter in Stanley Porter's book Linguistic Analysis of the Greek New Testament:
The aorist tense-form as the perfective aspect of πορευθέντες is used to establish the circumstance for the action of the finite verb of the primary clause, μαθητεύσατε. This circumstance is one of “going.” Within the secondary embedded structure forming an Adjunct, placed before the Predicator of the primary clause, it logically indicates background information to the command: going is background to the making of disciples.31 There is nothing here that minimizes the Great Commission to a suggestion. To the contrary, the syntactical structure retains the focus upon the making of disciples, which is at the syntactical heart of this command because it identifies the lexis of the finite verb of the Predicator.
How one renders Matthew 28:19–20 is another issue entirely. The Greek structure of a secondary embedded clause as Adjunct and Predicator of the primary clause does not “share” mood, but an English rendering might find it convenient to put the two on a parallel semantic plane in given contextual circumstances. However, this is probably not the best explanation for this passage, despite the history of translation. One reason to alter the rendering is that too much has probably been made of “going” (as Wallace does) rather than on “making disciples.” A rendering with “going” indicated as in some way subordinate in focus to “make disciples” helps to avoid any misperceptions that might result from simply taking the English as if it represented Greek with two imperative forms. This is the way Robert Gundry renders the construction, the only commentator that I have found who does so: “Going, therefore, make disciples of all the nations".
Participles don't have agent markers like verbs. Here the going is already decided as it is a background adjunct information to the main instruction of making disciples. From the text alone it's not clear if the command or instruction of going is made by Jesus or the disciples themselves decided it; but it is clear from the context that Jesus is sending them. This is why people like Daniel Wallace translate the adverbial participle as an imperative verb (Go), fearing that the instruction of the great commission may not be interpreted as great suggestion as if the instruction is subordinate & incidental task to the self determined journey of the disciples. Some like Stanley Porter, Gundry don't see that way.