से is not always 'from'. It also acts as the instrument case postposition in Hindi. In this usage, it is usually translated as 'with' or 'by' but there isn't a 1-1 correspondence.
For example, you have 'मैं काम से मुंबई जा रहा हूँ - I'm going to Mumbai for work.
So, the literal translation of the above sentence is something like 'Keep your work with (limited to) your own work'.
You use अपना when you want to refer back to the subject of the sentence/clause.
For example, नेहा अपना काम करती है (Neha does her work). The subject of the sentence is 'Neha'. The pronoun 'her' is also referring to Neha. So, we translate it as अपना.
'Do your work' is an imperative sentence (ie, a sentence that is either a request or a command). Imperative sentences have 'you' (तू, तुम or आप ) as the implicit subject. So, when we want to say 'your' which is referring to the subject, we need to use अपना.