There are three main conditions that one needs to fulfill in order to permit the selection of one object from another: 1) One must take the desired element (ochel) from the undesired (p’solet); taking p’solet from ochel is forbidden. 2) One must plan to use the ochel in the near future. 3) One may not use a special utensil to facilitate the selecting. Since you will not use the kedushat shvi’it remnants that you separate in the near future, condition #2 seems to be absent in your case.
To deal with this problem, we have to analyze conditon #1. Is it that only separating ochel from p’solet is permitted and other things are forbidden, or is that p’solet from ochel is forbidden and other things are permitted? A difference between the two possibilities is when one takes ochel from ochel, separating two things that will both be used at the same time in the future, but not immediately. On this point, the Pri Megadim[4] raises the possibility of leniency, but the Bi’ur Halacha[5] rejects the possibility and rules that if that which is removed will be used only significantly later, it is forbidden.
However, our case is one of separating p’solet from p’solet in a manner that neither will be used even in the future, and the Bi’ur Halacha agrees that it is permitted to do so. The reason this case is more lenient has to do with the definition of borer as a positive act. When one separates p’solet from ochel, the act is positive because it leaves an improved ochel behind. However, when both elements are thrown out, the fact that they are separated in the process is not positive in a significant manner.
This is one of the bases for permitting one to pour an undesired mixture of liquid and solid pieces into the sink even though the liquid will go down the drain and the solid pieces will be held back by the sieve-like drain cover. Rav S.Z. Auerbach[6] says that since both things are being discarded, the fact that they are separated in the process does not make the act borer. One could claim that the same is true in our case, in which one plans to put the two types of discarded food in two different garbage receptacles.
Despite the reasonable halachic basis for permitting separating the holy and non-holy unwanted leftovers,[7] several contemporary poskim were unwilling to permit it practically.[8] The matter may depend on the logic behind a Shemitta receptacle. Is it that one may discard kedushat shvi’it food but because of its holiness one should do so in a respectful manner?[9] Or is it that one has no right to waste Shemitta produce that is fit to eat, and so one puts it aside so that he can, at least in theory, eat it later? If the latter is the case, then removing kedushat shvi’it from other food is like selecting ochel from p’solet for non-immediate use, which is forbidden.[10] We heard in the name of Rav H. Schachter that the fact that the food requires a specific halachic process might[11] make the selection halachically significant and therefore a problem.
In any case, one should consider the following. According to our mentor, Rav Shaul Yisraeli, it is sufficient to put the Shemitta food in a bag before throwing it in the regular garbage. Whether one accepts this view or accepts the stringency of having a receptacle where the food will rot first, one may put non-Shemitta garbage along with the Shemitta remnants as long as the former is not already decomposing or will otherwise disgrace the Shemitta food. Therefore, there is no halachic need to separate the two types, and he can put the whole mixture in any non-disgraceful location.