Bhashya
त्वच एव सकाशात् अस्य पुरुषस्य रुधिरं प्रस्यन्दि,वनस्पतेस्त्वचः उत्पटः- त्वच एव उत्स्फुटति यस्मात्; एवंसर्वं समानमेव वनस्पतेः पुरुषस्य च ; तस्मात् आतृण्णात्हिंसितात् प्रैति तत् रुधिरं निर्गच्छति, वृक्षादिव आहतात्छिन्नात् रसः ॥
In plain words
'From the skin' just means: the blood in this body comes out through the skin, that's the bursting-out being spoken of — it breaks out through the skin itself. And here's the whole point: the tree and the person work exactly the same way. So when the verse says 'from what is torn', it means from an injury — that's where blood comes out. And 'from a tree that is struck' just means a tree that has been cut — that's where sap comes out.
Close to the Sanskrit
'From the skin alone' — from the vicinity of this person's skin, blood flows; 'from the skin comes the bursting-out' [means]: it is from the skin itself that it bursts forth, since — thus everything is exactly the same for the tree and for the person. 'Therefore from what is torn' [means] from what is injured, [blood] issues forth, that blood comes out; 'like from a tree that is struck' [means] from what is cut, [there flows] sap.