You must be doing something wrong since it works fine for me:

$ ls
BreastCnAPmiRNAsID.txt  tarbaseData.txt
$ cat BreastCnAPmiRNAsID.txt 
hsa-miR-4700-5p
hsa-miR-300
hsa-miR-381
hsa-miR-4803
$ cat tarbaseData.txt 
ENSG00000005175    RPAP3    hsa-miR-3199    Homo sapiens    293S    Ki
+dney    NA    HITS-CLIP    POSITIVE    DIRECT    DOWN    treatment:em
+etine
ENSG00000005175    RPAP3    hsa-miR-342-3p    Homo sapiens    HELA    
+Cervix    Cancer/Malignant    HITS-CLIP    POSITIVE    DIRECT    DOWN
+    Hela cells were treated with control shRNA.
ENSG00000005175    RPAP3    hsa-miR-381-3p    Homo sapiens    HS5    B
+one Marrow    Normal/Primary    HITS-CLIP    POSITIVE    DIRECT    DO
+WN    NA
ENSG00000005187    ACSM3    hsa-miR-196a-5p    Homo sapiens    EF3DAGO
+2    NA    Normal/Primary    PAR-CLIP    POSITIVE    DIRECT    DOWN  
+  NA
$ grep -f BreastCnAPmiRNAsID.txt tarbaseData.txt > output.txt
$ cat output.txt 
ENSG00000005175    RPAP3    hsa-miR-381-3p    Homo sapiens    HS5    B
+one Marrow    Normal/Primary    HITS-CLIP    POSITIVE    DIRECT    DO
+WN    NA
$
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