A good option for your specific example may be superfluous. From Oxford Dictionaries Online:
Unnecessary, especially through being more than enough.
I think the "more than enough" connotations make sense for something that used to be necessary, but is now holding you back. In your example this would be:
Stop writing encores that sound like the first one, you're just rearranging the words
Give birth to new comings and with them comes what once feed you with essentials
So sever all those superfluous umbilical cords
This, to me, implies more that the umbilical cord is no longer useful than that it has necessary become actively harmful, though I think the implication of any unnecessary cord is probably that it is likely to trip you up and hold you back.
You could also use the adjective surfeiting here. It's relatively rare, but appropriately poetical and has almost your exact intended meaning. From the Oxford English Dictionary1, with a couple of relevant attestations:
1 That causes surfeit; that produces a state of surfeit or satiety. Frequently fig. and in figurative contexts.
1576 T. BEDINGFIELD tr. G. Cardano Comforte (new ed.) iii. sig. J.viiiv He desyreth to sleape, whiche is not easlye had his stomacke beinge ouercharged wyth a surfytinge supper.
. . .
1995 Sun Herald (Sydney) (Nexis) 16 July 124 The fugal finale of the Verdi was akin to a tingling sorbet at the end of a refreshing but not surfeiting meal.
Of course this adjective is derived from surfeit, defined by Oxford Dictionaries Online (the free one) as
NOUN (plural surfeits)
1. usually in singular An excessive amount of something.
. . .
VERB (surfeited, surfeits, surfeiting)
[WITH OBJECT] (usually be surfeited with)
1. Cause (someone) to desire no more of something as a result of having consumed or done it to excess.
Shakespeare has a somewhat famous example of using surfeit to mean "too much of a good thing":
If music be the food of love, play on.
Give me excess of it that, surfeiting,
The appetite may sicken, and so die.
—Twelfth Night, 1.1, 1-3
This fits your desired meaning very well: Music, food, drink, and so forth are all good for you in moderation, but if you have a surfeit of them or surfeit on them then they become bad for you. In adjectival terms, we could say that you have had a surfeiting amount, or that the thing itself is surfeiting. In your example it would be
So sever all those surfeiting umbilical cords
Here, the implication is not just that the umbilical cord is holding you back, but that it is continuing to feed you unnecessarily, to the point of being harmful. Note that this would be a slightly different harm, however, than being connected to a rotting placenta post-birth.
1 "surfeiting, adj." OED Online, Oxford University Press, June 2017, www.oed.com/view/Entry/194903. Note that the OED is different from the above-cited ODO, and unfortunately is a prescription service (behind a paywall). However, many folks, especially in the UK, will have access through their local public library, and most students should be able to access through their institution's library. More info here: http://public.oed.com/about/free-oed/