First of all, I want you to learn the word, Sashi Men. It most of the time refers to a small men cut.
However, it also refers to a men cut that is not considered to be correct. It is very confusing when you hear this word, but now you will know the difference.
When you are told to perform sashi men during training, you are asked to execute small men cuts.
If a sensei or someone tells you not to strike sashi men, they are referring a particular small men cut, which I am going to explain now.
Sashi men (Incorrect small men cut):
Sashi means "to thrust". So Sashi men is not a cut, but it looks like a thrust because your shinai does not have up and down movement (cutting movement).
Your shinai should move up and down to "cut" your opponent's men. That is why we bring up our shinai right above our head and bring our shinai down. This is the basic cutting movement.
Thus, even though when you are executing a small men cut, your shinai should include this cutting movement. In sashi men, however, there is no such movement involved. That is why it is considered to be an incorrect way to strike a men.
In my dojo when I was a kid, we did not use the word "sashi men" but "chii-saku men" as a command (Strike Men) and "chiisai men" as a noun (small men). These are the terms used at my dojo when I was a kid so I am not sure what words any other dojos use for small men.
Anyway, you should remember two ways of using the term, sashi men. One refers to a small men and another refers to an incorrect men cut.
There are many ways of striking a small men unlike a big men cut. In the video there are 4 men cuts including a basic small men cut introduced. Thus, try to learn various kinds of small men cuts.
The video is in Spanish too, thanks to Guatemalan Kendo Association. Please enjoy the English and Spanish Kendo video.
Hope it helps.