Verse 11

chittasya shuddhaye karma na tu vastuupalabdhaye .
vastusiddhirvichaareNa na ki.nchitkarmakoTibhiH

Karma is intended for purification of the mind, not for understanding the nature of an object. Knowledge can be obtained only by reflection; not even a little bit of it can be known by performing even a crore of karma's.

(His Holiness discusses both sides of the argument here for clarity, although he does not directly elaborate on the actual verse.)

It is obvious from verse 10 that yogArudhatva is obtained by giving up ALL forms of karma, even the nitya karma's. It may be objected by quoting the sruti, where the sruti says: "One should perform the agnihotra sacrifice, the darsa and purnamAsa sacrifices all through life (Taitt). Similar verses are to be found in the Isa. Up. also. So, the argument is that giving up all karmas is a sin. The counter argument and the coreect way of reading them is: The sruti statements are directed only to a person of impure mind, i.e., to a person who has not cultivated complete detachment. A mantra of the Isa. Up says: "For one who thinks of himeself as a mere man (without awareness of the Atman), there is no other go except to do the karma." Again it is said: 

na karmanA na prajayA dhanena tyAgenaike
amrtatvamAnasuh; samnyAsayogAdyatayassuddhastvAh | 

Those rare spirits attained immortality not by karmas, not by progeny, not by gifts but these holy ones of pure nature did so by the force of their samnyAsa.

Similarly, the srutis clearly say that sacrifices and other karmas are inferior and are like weak boats . To consider them as superior is to get further entangled. Sruti texts like yadahareva virajet tadahareva pravjet: "One should become a samnyAsin the moment one gets vairAgya", which prescribe the adoption of samnyAsa, are in place here and they discountenance the performance of karmas. Hence it is clear from Sri BhagavatpAda's this sloka, that karmas do not possess the capacity to lead to the supreme objective of liberation and that, as means to purification of mind, they are external auxiliaries.

Follow up discussion on the list: 

This is a part of the discussion of HH on verse 11 of the vivekachUdAmani. I could not fully understand the reference to the "weak boat" at that time. Now, by His grace, I have come across a meaning/discussion of the PraNavam AUM. It greatly clarifies the reference. The following is from the Siva Purana. Ch 17. ver. 2 - 8

The symbol AUM means an excellent boat to cross the ocean of worldy exixtence. Pra = of the Prakrti i.e., the world evolved out of it. Navam - nAvAm varam - an excellent boat. 

Or Pranava may mean: "that which leads to new knowledge". After annihilating all actions it gives the persons who repeat the mantra or worship, a fresh knowledge of the pure soul.