The phrasing is ambiguous but becomes clear from context. The reference to "big-D" disciples actually introduces the ambiguity. If the printer had left it "little-d" disciples then the meaning would be clear. The "thing which ye have done" is a reference to partaking of the wine. By introducing the "big-D" disciple term it can change the entire thing to be "the thing which ye have done" is to pass the sacrament, rather than to partake of it.
Well, the "thing which ye have done" that prompts the Lord to proclaim "Blessed are ye" is to have symbolically partaken of His blood. They have a part of Him by having eaten of His flesh and drank of His blood. They are now among those who demonstrate they hunger and thirst after righteousness. They are disciples indeed. Followers of the Master. Obedient to Him and willing to take His name upon them.
This is again identified as a "witness unto the Father" rather than a witness unto anyone else. It is not even a witness unto Christ. Nor is it a witness unto one another. It is a witness unto the Father.
This sacred event marks the testimony of faith by those who follow the Lord as a witness to the Father. These people prove they have faith in, and will obey His Son. The Father provided the Son as the Redeemer of all mankind. The only way back into the exalted state of the Father is through the saving sacrifice of the Son. It was the Son who opened the door for that return by the burdens He assumed while in His mortal body. He came under the same circumstances we did. He was separated from the Father by the veil. He suffered weaknesses of the body. He suffered the temptations of mankind, and He gave them no heed. (D&C 20: 22.) This made it possible for Him to bring many others to glory. (Heb. 2: 10.)
To have part in His glory, we must partake of His flesh and blood. Both symbolically by our own bodies being made a living sacrifice, (Romans 12: 1) and through ordinance by partaking of the symbols of His life, death, resurrection. For the body of Christ rose from the dead, and we have that same hope. If we are to follow Him, we must be like Him. Taking upon ourselves His flesh and blood is not optional. It must be done to testify to the Father, who alone accepts us into His family. If we think to take upon us the name of Christ, but fail to have this witness before the Father, then we have failed to secure the required testimony before the Father.
This is a required process for those who are His.